1 Packages and Reference

We use BAS packages. We proceeded with reference to this example.

Also, I give my sincere gratitude to KKH.

library(BAS)
library(tidyverse)
library(plotly)

2 Preprocessing

colnames(original_data)
##  [1] "X1"                    "idx"                   "population"           
##  [4] "householdsize"         "racepctblack"          "racePctWhite"         
##  [7] "racePctAsian"          "racePctHisp"           "agePct12t29"          
## [10] "agePct65up"            "numbUrban"             "pctUrban"             
## [13] "medIncome"             "pctWWage"              "pctWFarmSelf"         
## [16] "pctWInvInc"            "pctWSocSec"            "pctWPubAsst"          
## [19] "pctWRetire"            "medFamInc"             "whitePerCap"          
## [22] "blackPerCap"           "indianPerCap"          "AsianPerCap"          
## [25] "OtherPerCap"           "HispPerCap"            "NumUnderPov"          
## [28] "PctPopUnderPov"        "PctLess9thGrade"       "PctBSorMore"          
## [31] "PctUnemployed"         "PctEmploy"             "PctEmplManu"          
## [34] "PctEmplProfServ"       "PctOccupMgmtProf"      "MalePctNevMarr"       
## [37] "TotalPctDiv"           "PersPerFam"            "PctFam2Par"           
## [40] "PctWorkMom"            "PctKidsBornNeverMar"   "NumImmig"             
## [43] "PctImmigRecent"        "PctRecentImmig"        "PctSpeakEnglOnly"     
## [46] "PctNotSpeakEnglWell"   "PctLargHouseFam"       "PersPerOccupHous"     
## [49] "PersPerOwnOccHous"     "PersPerRentOccHous"    "PctPersOwnOccup"      
## [52] "PctPersDenseHous"      "PctHousLess3BR"        "MedNumBR"             
## [55] "HousVacant"            "PctHousOccup"          "PctHousOwnOcc"        
## [58] "PctVacantBoarded"      "PctVacMore6Mos"        "MedYrHousBuilt"       
## [61] "PctHousNoPhone"        "PctWOFullPlumb"        "OwnOccLowQuart"       
## [64] "OwnOccMedVal"          "OwnOccHiQuart"         "RentLowQ"             
## [67] "RentMedian"            "RentHighQ"             "MedRent"              
## [70] "MedRentPctHousInc"     "MedOwnCostPctInc"      "MedOwnCostPctIncNoMtg"
## [73] "NumInShelters"         "NumStreet"             "PctForeignBorn"       
## [76] "PctBornSameState"      "PctSameHouse85"        "PctSameCity85"        
## [79] "PctSameState85"        "LandArea"              "PopDens"              
## [82] "PctUsePubTrans"        "LemasPctOfficDrugUn"   "agePct22t29"          
## [85] "murdPerPop"            "rapesPerPop"           "robbbPerPop"          
## [88] "assaultPerPop"         "burglPerPop"           "larcPerPop"           
## [91] "autoTheftPerPop"       "arsonsPerPop"
data = subset(original_data, select = -c(X1, idx)) 

data %>% head()
## # A tibble: 6 x 90
##   population householdsize racepctblack racePctWhite racePctAsian racePctHisp
##        <dbl>         <dbl>        <dbl>        <dbl>        <dbl>       <dbl>
## 1    -0.977          1.18        -0.559        0.475        0.856      -0.416
## 2    -0.214          0.337       -0.599        0.706        0.172      -0.487
## 3     0.0618        -0.830       -0.603        0.631        0.170      -0.384
## 4    -0.595         -0.920       -0.536        0.814       -0.485      -0.497
## 5    -1.05           0.158       -0.618        0.316       -0.335      -0.509
## 6     1.88          -0.770       -0.479        0.711       -0.396      -0.480
## # … with 84 more variables: agePct12t29 <dbl>, agePct65up <dbl>,
## #   numbUrban <dbl>, pctUrban <dbl>, medIncome <dbl>, pctWWage <dbl>,
## #   pctWFarmSelf <dbl>, pctWInvInc <dbl>, pctWSocSec <dbl>, pctWPubAsst <dbl>,
## #   pctWRetire <dbl>, medFamInc <dbl>, whitePerCap <dbl>, blackPerCap <dbl>,
## #   indianPerCap <dbl>, AsianPerCap <dbl>, OtherPerCap <dbl>, HispPerCap <dbl>,
## #   NumUnderPov <dbl>, PctPopUnderPov <dbl>, PctLess9thGrade <dbl>,
## #   PctBSorMore <dbl>, PctUnemployed <dbl>, PctEmploy <dbl>, PctEmplManu <dbl>,
## #   PctEmplProfServ <dbl>, PctOccupMgmtProf <dbl>, MalePctNevMarr <dbl>,
## #   TotalPctDiv <dbl>, PersPerFam <dbl>, PctFam2Par <dbl>, PctWorkMom <dbl>,
## #   PctKidsBornNeverMar <dbl>, NumImmig <dbl>, PctImmigRecent <dbl>,
## #   PctRecentImmig <dbl>, PctSpeakEnglOnly <dbl>, PctNotSpeakEnglWell <dbl>,
## #   PctLargHouseFam <dbl>, PersPerOccupHous <dbl>, PersPerOwnOccHous <dbl>,
## #   PersPerRentOccHous <dbl>, PctPersOwnOccup <dbl>, PctPersDenseHous <dbl>,
## #   PctHousLess3BR <dbl>, MedNumBR <dbl>, HousVacant <dbl>, PctHousOccup <dbl>,
## #   PctHousOwnOcc <dbl>, PctVacantBoarded <dbl>, PctVacMore6Mos <dbl>,
## #   MedYrHousBuilt <dbl>, PctHousNoPhone <dbl>, PctWOFullPlumb <dbl>,
## #   OwnOccLowQuart <dbl>, OwnOccMedVal <dbl>, OwnOccHiQuart <dbl>,
## #   RentLowQ <dbl>, RentMedian <dbl>, RentHighQ <dbl>, MedRent <dbl>,
## #   MedRentPctHousInc <dbl>, MedOwnCostPctInc <dbl>,
## #   MedOwnCostPctIncNoMtg <dbl>, NumInShelters <dbl>, NumStreet <dbl>,
## #   PctForeignBorn <dbl>, PctBornSameState <dbl>, PctSameHouse85 <dbl>,
## #   PctSameCity85 <dbl>, PctSameState85 <dbl>, LandArea <dbl>, PopDens <dbl>,
## #   PctUsePubTrans <dbl>, LemasPctOfficDrugUn <dbl>, agePct22t29 <dbl>,
## #   murdPerPop <dbl>, rapesPerPop <dbl>, robbbPerPop <dbl>,
## #   assaultPerPop <dbl>, burglPerPop <dbl>, larcPerPop <dbl>,
## #   autoTheftPerPop <dbl>, arsonsPerPop <dbl>

3 murdPerPop

y_name = 'murdPerPop'

3.1 Model fit

f = paste(y_name, " ~ . -murdPerPop -rapesPerPop -robbbPerPop -assaultPerPop -burglPerPop -larcPerPop -autoTheftPerPop -arsonsPerPop")

fit.gprior = bas.lm(f,
                    data = data,
                    method = "MCMC", # better than default "BAS"
                                     # for large p
                   prior = "ZS-null", # default
                                      # "JZS" also can use
                   modelprior = uniform(),
                   include.always = ~1,
                   MCMC.iterations = 100000)
## Warning in bas.lm(f, data = data, method = "MCMC", prior = "ZS-null", modelprior
## = uniform(), : dropping 313 rows due to missing data
plot(fit.gprior, ask = F)

3.2 model result

summary(fit.gprior)
##                       P(B != 0 | Y)  model 1      model 2      model 3
## Intercept                   1.00000   1.0000   1.00000000 1.000000e+00
## population                  0.72241   1.0000   0.00000000 0.000000e+00
## householdsize               0.09946   0.0000   0.00000000 0.000000e+00
## racepctblack                0.98390   1.0000   1.00000000 1.000000e+00
## racePctWhite                0.70205   0.0000   1.00000000 0.000000e+00
## racePctAsian                0.10683   0.0000   0.00000000 0.000000e+00
## racePctHisp                 0.10775   0.0000   0.00000000 0.000000e+00
## agePct12t29                 0.33904   1.0000   0.00000000 0.000000e+00
## agePct65up                  0.11923   0.0000   0.00000000 0.000000e+00
## numbUrban                   0.08325   0.0000   0.00000000 0.000000e+00
## pctUrban                    0.08891   0.0000   0.00000000 0.000000e+00
## medIncome                   0.11219   0.0000   0.00000000 0.000000e+00
## pctWWage                    0.37848   0.0000   0.00000000 0.000000e+00
## pctWFarmSelf                0.07752   0.0000   0.00000000 0.000000e+00
## pctWInvInc                  0.09398   0.0000   0.00000000 0.000000e+00
## pctWSocSec                  0.17205   0.0000   0.00000000 0.000000e+00
## pctWPubAsst                 0.09952   0.0000   0.00000000 0.000000e+00
## pctWRetire                  0.33569   0.0000   0.00000000 1.000000e+00
## medFamInc                   0.40717   0.0000   1.00000000 0.000000e+00
## whitePerCap                 0.43736   0.0000   1.00000000 0.000000e+00
## blackPerCap                 0.06729   0.0000   0.00000000 0.000000e+00
## indianPerCap                0.07136   0.0000   0.00000000 0.000000e+00
## AsianPerCap                 0.07313   0.0000   0.00000000 0.000000e+00
## OtherPerCap                 0.06845   0.0000   0.00000000 0.000000e+00
## HispPerCap                  0.08464   0.0000   0.00000000 0.000000e+00
## NumUnderPov                 0.63998   1.0000   0.00000000 0.000000e+00
## PctPopUnderPov              0.32094   0.0000   0.00000000 0.000000e+00
## PctLess9thGrade             0.10595   0.0000   0.00000000 1.000000e+00
## PctBSorMore                 0.08597   0.0000   0.00000000 0.000000e+00
## PctUnemployed               0.16859   0.0000   0.00000000 0.000000e+00
## PctEmploy                   0.25523   0.0000   0.00000000 0.000000e+00
## PctEmplManu                 0.44242   0.0000   1.00000000 1.000000e+00
## PctEmplProfServ             0.09205   0.0000   0.00000000 0.000000e+00
## PctOccupMgmtProf            0.09580   0.0000   0.00000000 0.000000e+00
## MalePctNevMarr              0.16312   0.0000   0.00000000 0.000000e+00
## TotalPctDiv                 0.17850   0.0000   0.00000000 0.000000e+00
## PersPerFam                  0.32913   1.0000   0.00000000 0.000000e+00
## PctFam2Par                  0.85712   1.0000   1.00000000 1.000000e+00
## PctWorkMom                  0.93975   1.0000   1.00000000 1.000000e+00
## PctKidsBornNeverMar         0.12638   0.0000   0.00000000 0.000000e+00
## NumImmig                    0.10957   0.0000   0.00000000 0.000000e+00
## PctImmigRecent              0.07149   0.0000   0.00000000 0.000000e+00
## PctRecentImmig              0.11983   0.0000   0.00000000 0.000000e+00
## PctSpeakEnglOnly            0.84790   1.0000   1.00000000 0.000000e+00
## PctNotSpeakEnglWell         0.46304   0.0000   0.00000000 0.000000e+00
## PctLargHouseFam             0.13795   0.0000   0.00000000 1.000000e+00
## PersPerOccupHous            0.17992   0.0000   0.00000000 0.000000e+00
## PersPerOwnOccHous           0.63062   1.0000   0.00000000 1.000000e+00
## PersPerRentOccHous          0.12389   0.0000   0.00000000 0.000000e+00
## PctPersOwnOccup             0.18349   0.0000   0.00000000 1.000000e+00
## PctPersDenseHous            0.91608   1.0000   1.00000000 1.000000e+00
## PctHousLess3BR              0.15205   0.0000   0.00000000 0.000000e+00
## MedNumBR                    0.14372   0.0000   0.00000000 0.000000e+00
## HousVacant                  0.59136   0.0000   1.00000000 0.000000e+00
## PctHousOccup                0.12012   0.0000   0.00000000 0.000000e+00
## PctHousOwnOcc               0.27723   0.0000   0.00000000 0.000000e+00
## PctVacantBoarded            0.99963   1.0000   1.00000000 1.000000e+00
## PctVacMore6Mos              0.25100   0.0000   0.00000000 1.000000e+00
## MedYrHousBuilt              0.20321   0.0000   0.00000000 0.000000e+00
## PctHousNoPhone              0.07940   0.0000   0.00000000 0.000000e+00
## PctWOFullPlumb              0.88715   1.0000   1.00000000 1.000000e+00
## OwnOccLowQuart              0.11106   0.0000   0.00000000 0.000000e+00
## OwnOccMedVal                0.10642   0.0000   0.00000000 0.000000e+00
## OwnOccHiQuart               0.11107   0.0000   0.00000000 0.000000e+00
## RentLowQ                    0.08455   0.0000   0.00000000 0.000000e+00
## RentMedian                  0.09244   0.0000   0.00000000 1.000000e+00
## RentHighQ                   0.10569   0.0000   0.00000000 0.000000e+00
## MedRent                     0.11882   0.0000   1.00000000 0.000000e+00
## MedRentPctHousInc           0.18653   0.0000   0.00000000 0.000000e+00
## MedOwnCostPctInc            0.08294   0.0000   0.00000000 0.000000e+00
## MedOwnCostPctIncNoMtg       0.06575   0.0000   0.00000000 0.000000e+00
## NumInShelters               0.16761   0.0000   0.00000000 0.000000e+00
## NumStreet                   0.76426   1.0000   1.00000000 1.000000e+00
## PctForeignBorn              0.14487   0.0000   0.00000000 0.000000e+00
## PctBornSameState            0.11327   0.0000   0.00000000 0.000000e+00
## PctSameHouse85              0.12127   0.0000   0.00000000 1.000000e+00
## PctSameCity85               0.08401   0.0000   0.00000000 0.000000e+00
## PctSameState85              0.08189   0.0000   1.00000000 0.000000e+00
## LandArea                    0.81535   1.0000   1.00000000 1.000000e+00
## PopDens                     0.26511   0.0000   0.00000000 0.000000e+00
## PctUsePubTrans              0.28357   0.0000   0.00000000 0.000000e+00
## LemasPctOfficDrugUn         0.06621   0.0000   0.00000000 0.000000e+00
## agePct22t29                 0.13927   0.0000   0.00000000 0.000000e+00
## BF                               NA   1.0000   0.01090494 8.797887e-06
## PostProbs                        NA   0.0009   0.00050000 5.000000e-04
## R2                               NA   0.5793   0.57980000 5.779000e-01
## dim                              NA  15.0000  17.00000000 1.800000e+01
## logmarg                          NA 775.2954 770.77690577 7.636544e+02
##                            model 4      model 5
## Intercept               1.00000000   1.00000000
## population              1.00000000   1.00000000
## householdsize           0.00000000   0.00000000
## racepctblack            1.00000000   1.00000000
## racePctWhite            0.00000000   1.00000000
## racePctAsian            0.00000000   0.00000000
## racePctHisp             0.00000000   0.00000000
## agePct12t29             0.00000000   0.00000000
## agePct65up              0.00000000   0.00000000
## numbUrban               0.00000000   0.00000000
## pctUrban                0.00000000   0.00000000
## medIncome               1.00000000   0.00000000
## pctWWage                0.00000000   1.00000000
## pctWFarmSelf            0.00000000   0.00000000
## pctWInvInc              0.00000000   0.00000000
## pctWSocSec              0.00000000   0.00000000
## pctWPubAsst             0.00000000   0.00000000
## pctWRetire              0.00000000   1.00000000
## medFamInc               1.00000000   0.00000000
## whitePerCap             1.00000000   0.00000000
## blackPerCap             0.00000000   0.00000000
## indianPerCap            0.00000000   0.00000000
## AsianPerCap             0.00000000   0.00000000
## OtherPerCap             0.00000000   0.00000000
## HispPerCap              0.00000000   0.00000000
## NumUnderPov             1.00000000   1.00000000
## PctPopUnderPov          0.00000000   0.00000000
## PctLess9thGrade         0.00000000   0.00000000
## PctBSorMore             0.00000000   0.00000000
## PctUnemployed           0.00000000   0.00000000
## PctEmploy               0.00000000   0.00000000
## PctEmplManu             0.00000000   0.00000000
## PctEmplProfServ         0.00000000   1.00000000
## PctOccupMgmtProf        0.00000000   0.00000000
## MalePctNevMarr          0.00000000   0.00000000
## TotalPctDiv             0.00000000   0.00000000
## PersPerFam              0.00000000   1.00000000
## PctFam2Par              1.00000000   1.00000000
## PctWorkMom              1.00000000   1.00000000
## PctKidsBornNeverMar     0.00000000   0.00000000
## NumImmig                0.00000000   0.00000000
## PctImmigRecent          0.00000000   0.00000000
## PctRecentImmig          0.00000000   0.00000000
## PctSpeakEnglOnly        1.00000000   1.00000000
## PctNotSpeakEnglWell     0.00000000   0.00000000
## PctLargHouseFam         0.00000000   0.00000000
## PersPerOccupHous        0.00000000   0.00000000
## PersPerOwnOccHous       0.00000000   1.00000000
## PersPerRentOccHous      0.00000000   0.00000000
## PctPersOwnOccup         0.00000000   0.00000000
## PctPersDenseHous        1.00000000   1.00000000
## PctHousLess3BR          0.00000000   0.00000000
## MedNumBR                0.00000000   0.00000000
## HousVacant              0.00000000   0.00000000
## PctHousOccup            0.00000000   0.00000000
## PctHousOwnOcc           1.00000000   0.00000000
## PctVacantBoarded        1.00000000   1.00000000
## PctVacMore6Mos          0.00000000   0.00000000
## MedYrHousBuilt          0.00000000   0.00000000
## PctHousNoPhone          0.00000000   0.00000000
## PctWOFullPlumb          1.00000000   1.00000000
## OwnOccLowQuart          0.00000000   0.00000000
## OwnOccMedVal            0.00000000   0.00000000
## OwnOccHiQuart           0.00000000   0.00000000
## RentLowQ                0.00000000   0.00000000
## RentMedian              0.00000000   0.00000000
## RentHighQ               0.00000000   0.00000000
## MedRent                 0.00000000   0.00000000
## MedRentPctHousInc       0.00000000   0.00000000
## MedOwnCostPctInc        0.00000000   0.00000000
## MedOwnCostPctIncNoMtg   0.00000000   0.00000000
## NumInShelters           0.00000000   0.00000000
## NumStreet               1.00000000   1.00000000
## PctForeignBorn          0.00000000   0.00000000
## PctBornSameState        0.00000000   0.00000000
## PctSameHouse85          0.00000000   0.00000000
## PctSameCity85           0.00000000   0.00000000
## PctSameState85          0.00000000   0.00000000
## LandArea                1.00000000   1.00000000
## PopDens                 0.00000000   0.00000000
## PctUsePubTrans          0.00000000   0.00000000
## LemasPctOfficDrugUn     0.00000000   0.00000000
## agePct22t29             0.00000000   0.00000000
## BF                      0.01629809   0.06800977
## PostProbs               0.00050000   0.00040000
## R2                      0.57870000   0.58190000
## dim                    16.00000000  18.00000000
## logmarg               771.17873775 772.60734105

top 5 model

3.3 Visualization of the Model Space

image(fit.gprior, rotate=F)

3.4 Posterior Distributions of Coefficients

coef.gprior = coef(fit.gprior)
coef.gprior
## 
##  Marginal Posterior Summaries of Coefficients: 
## 
##  Using  BMA 
## 
##  Based on the top  23979 models 
##                        post mean   post SD     post p(B != 0)
## Intercept               5.968e+00   1.353e-01   1.000e+00    
## population              1.546e+00   1.257e+00   7.224e-01    
## householdsize          -3.540e-03   1.467e-01   9.946e-02    
## racepctblack            2.454e+00   8.287e-01   9.839e-01    
## racePctWhite           -1.130e+00   9.408e-01   7.020e-01    
## racePctAsian           -2.100e-02   1.276e-01   1.068e-01    
## racePctHisp            -3.052e-02   2.288e-01   1.077e-01    
## agePct12t29            -2.317e-01   4.176e-01   3.390e-01    
## agePct65up             -3.539e-02   2.279e-01   1.192e-01    
## numbUrban               1.152e-02   1.113e-01   8.325e-02    
## pctUrban                3.569e-03   1.026e-01   8.891e-02    
## medIncome              -1.645e-02   4.682e-01   1.122e-01    
## pctWWage               -4.788e-01   7.663e-01   3.785e-01    
## pctWFarmSelf            5.406e-03   5.384e-02   7.752e-02    
## pctWInvInc             -2.073e-02   1.591e-01   9.398e-02    
## pctWSocSec             -1.527e-01   4.560e-01   1.721e-01    
## pctWPubAsst             3.175e-02   1.671e-01   9.952e-02    
## pctWRetire             -1.511e-01   2.521e-01   3.357e-01    
## medFamInc              -8.236e-01   1.218e+00   4.072e-01    
## whitePerCap             6.038e-01   8.264e-01   4.374e-01    
## blackPerCap             1.715e-06   4.309e-02   6.729e-02    
## indianPerCap            1.371e-03   3.617e-02   7.136e-02    
## AsianPerCap             3.780e-03   4.543e-02   7.313e-02    
## OtherPerCap             6.224e-03   4.445e-02   6.845e-02    
## HispPerCap              9.400e-03   6.398e-02   8.464e-02    
## NumUnderPov            -1.503e+00   1.420e+00   6.400e-01    
## PctPopUnderPov          3.609e-01   6.536e-01   3.209e-01    
## PctLess9thGrade        -3.459e-02   1.622e-01   1.060e-01    
## PctBSorMore            -1.470e-02   1.285e-01   8.597e-02    
## PctUnemployed          -7.284e-02   2.115e-01   1.686e-01    
## PctEmploy               2.121e-01   4.525e-01   2.552e-01    
## PctEmplManu             1.730e-01   2.297e-01   4.424e-01    
## PctEmplProfServ        -1.928e-04   7.324e-02   9.205e-02    
## PctOccupMgmtProf        8.597e-03   1.254e-01   9.580e-02    
## MalePctNevMarr          8.435e-02   3.059e-01   1.631e-01    
## TotalPctDiv             8.672e-02   2.587e-01   1.785e-01    
## PersPerFam              4.240e-01   7.433e-01   3.291e-01    
## PctFam2Par             -1.371e+00   7.383e-01   8.571e-01    
## PctWorkMom             -6.935e-01   2.707e-01   9.397e-01    
## PctKidsBornNeverMar     5.712e-02   2.532e-01   1.264e-01    
## NumImmig               -3.712e-02   2.333e-01   1.096e-01    
## PctImmigRecent         -2.873e-03   5.037e-02   7.149e-02    
## PctRecentImmig          4.122e-02   1.893e-01   1.198e-01    
## PctSpeakEnglOnly        1.235e+00   7.657e-01   8.479e-01    
## PctNotSpeakEnglWell     6.086e-01   7.891e-01   4.630e-01    
## PctLargHouseFam         6.210e-02   2.675e-01   1.379e-01    
## PersPerOccupHous        1.841e-01   6.239e-01   1.799e-01    
## PersPerOwnOccHous      -8.745e-01   8.588e-01   6.306e-01    
## PersPerRentOccHous     -2.310e-02   2.348e-01   1.239e-01    
## PctPersOwnOccup        -1.532e-01   9.191e-01   1.835e-01    
## PctPersDenseHous        1.798e+00   7.949e-01   9.161e-01    
## PctHousLess3BR          7.144e-02   2.454e-01   1.520e-01    
## MedNumBR               -3.795e-02   1.211e-01   1.437e-01    
## HousVacant              2.908e-01   2.874e-01   5.914e-01    
## PctHousOccup           -2.391e-02   9.686e-02   1.201e-01    
## PctHousOwnOcc           3.618e-01   9.716e-01   2.772e-01    
## PctVacantBoarded        1.662e+00   2.014e-01   9.996e-01    
## PctVacMore6Mos         -8.467e-02   1.794e-01   2.510e-01    
## MedYrHousBuilt         -7.134e-02   1.814e-01   2.032e-01    
## PctHousNoPhone          1.702e-02   1.090e-01   7.940e-02    
## PctWOFullPlumb         -5.132e-01   2.528e-01   8.871e-01    
## OwnOccLowQuart         -3.963e-02   1.952e-01   1.111e-01    
## OwnOccMedVal           -2.816e-02   2.004e-01   1.064e-01    
## OwnOccHiQuart          -3.980e-02   1.862e-01   1.111e-01    
## RentLowQ               -2.464e-04   1.249e-01   8.455e-02    
## RentMedian             -2.468e-02   2.899e-01   9.244e-02    
## RentHighQ               3.896e-02   2.197e-01   1.057e-01    
## MedRent                 6.705e-02   3.212e-01   1.188e-01    
## MedRentPctHousInc       6.054e-02   1.602e-01   1.865e-01    
## MedOwnCostPctInc       -6.613e-03   7.213e-02   8.294e-02    
## MedOwnCostPctIncNoMtg   3.758e-03   4.882e-02   6.575e-02    
## NumInShelters           5.152e-02   1.465e-01   1.676e-01    
## NumStreet               4.202e-01   2.913e-01   7.643e-01    
## PctForeignBorn         -9.897e-02   3.406e-01   1.449e-01    
## PctBornSameState        2.618e-02   1.050e-01   1.133e-01    
## PctSameHouse85          3.637e-02   1.493e-01   1.213e-01    
## PctSameCity85           7.299e-03   8.567e-02   8.401e-02    
## PctSameState85          8.782e-03   7.263e-02   8.189e-02    
## LandArea                6.961e-01   4.091e-01   8.154e-01    
## PopDens                -1.461e-01   3.001e-01   2.651e-01    
## PctUsePubTrans          1.157e-01   2.237e-01   2.836e-01    
## LemasPctOfficDrugUn     4.894e-04   4.276e-02   6.621e-02    
## agePct22t29            -3.561e-02   1.429e-01   1.393e-01

3.4.1 individual plot

probne0 > 0.2

survivors = which(coef.gprior$probne0 > 0.2)
plot(coef.gprior, subset = survivors, ask = F)

3.4.2 coefficient plot

plot(confint(coef.gprior, parm = survivors))

## NULL

3.5 Prediction

muhat.bma <- fitted(fit.gprior, estimator = "BMA")
bma <- predict(fit.gprior, estimator = "BMA", newdata = data)

result_data = original_data %>%
  mutate(pred_y=bma$fit)

4 rapesPerPop

y_name = 'rapesPerPop'

4.1 Model fit

f = paste(y_name, " ~ . -murdPerPop -rapesPerPop -robbbPerPop -assaultPerPop -burglPerPop -larcPerPop -autoTheftPerPop -arsonsPerPop")

fit.gprior = bas.lm(f,
                    data = data,
                    method = "MCMC", # better than default "BAS"
                                     # for large p
                   prior = "ZS-null", # default
                                      # "JZS" also can use
                   modelprior = uniform(),
                   include.always = ~1,
                   MCMC.iterations = 100000)
## Warning in bas.lm(f, data = data, method = "MCMC", prior = "ZS-null", modelprior
## = uniform(), : dropping 313 rows due to missing data
plot(fit.gprior, ask = F)

4.2 model result

summary(fit.gprior)
##                       P(B != 0 | Y)    model 1    model 2      model 3  model 4
## Intercept                   1.00000   1.000000   1.000000 1.000000e+00   1.0000
## population                  0.17079   0.000000   0.000000 0.000000e+00   1.0000
## householdsize               0.12428   0.000000   0.000000 0.000000e+00   0.0000
## racepctblack                0.18891   0.000000   0.000000 0.000000e+00   1.0000
## racePctWhite                0.47841   0.000000   0.000000 1.000000e+00   0.0000
## racePctAsian                0.11505   0.000000   0.000000 0.000000e+00   0.0000
## racePctHisp                 0.73507   1.000000   1.000000 0.000000e+00   1.0000
## agePct12t29                 0.35788   0.000000   0.000000 1.000000e+00   0.0000
## agePct65up                  0.15857   0.000000   0.000000 0.000000e+00   0.0000
## numbUrban                   0.11212   0.000000   0.000000 0.000000e+00   0.0000
## pctUrban                    0.14196   0.000000   0.000000 0.000000e+00   0.0000
## medIncome                   0.36661   0.000000   0.000000 1.000000e+00   1.0000
## pctWWage                    0.16627   0.000000   0.000000 0.000000e+00   0.0000
## pctWFarmSelf                0.25505   0.000000   0.000000 0.000000e+00   0.0000
## pctWInvInc                  0.16440   0.000000   0.000000 0.000000e+00   0.0000
## pctWSocSec                  0.30785   0.000000   1.000000 1.000000e+00   1.0000
## pctWPubAsst                 0.17971   0.000000   0.000000 0.000000e+00   0.0000
## pctWRetire                  0.09631   0.000000   0.000000 1.000000e+00   0.0000
## medFamInc                   0.19363   0.000000   0.000000 0.000000e+00   0.0000
## whitePerCap                 0.13679   0.000000   1.000000 1.000000e+00   0.0000
## blackPerCap                 0.17823   0.000000   0.000000 0.000000e+00   0.0000
## indianPerCap                0.08147   1.000000   0.000000 0.000000e+00   0.0000
## AsianPerCap                 0.09725   0.000000   0.000000 0.000000e+00   0.0000
## OtherPerCap                 0.68301   1.000000   0.000000 1.000000e+00   1.0000
## HispPerCap                  0.17658   0.000000   1.000000 0.000000e+00   0.0000
## NumUnderPov                 0.13854   0.000000   0.000000 0.000000e+00   0.0000
## PctPopUnderPov              0.15234   0.000000   0.000000 1.000000e+00   1.0000
## PctLess9thGrade             0.99785   1.000000   1.000000 1.000000e+00   1.0000
## PctBSorMore                 0.17624   0.000000   0.000000 0.000000e+00   0.0000
## PctUnemployed               0.66368   1.000000   1.000000 0.000000e+00   1.0000
## PctEmploy                   0.19160   1.000000   0.000000 0.000000e+00   0.0000
## PctEmplManu                 0.12737   0.000000   0.000000 0.000000e+00   0.0000
## PctEmplProfServ             0.09685   0.000000   0.000000 0.000000e+00   0.0000
## PctOccupMgmtProf            0.28694   0.000000   0.000000 0.000000e+00   0.0000
## MalePctNevMarr              0.12311   0.000000   0.000000 0.000000e+00   0.0000
## TotalPctDiv                 0.99988   1.000000   1.000000 1.000000e+00   1.0000
## PersPerFam                  0.29158   1.000000   1.000000 0.000000e+00   0.0000
## PctFam2Par                  0.11799   0.000000   0.000000 0.000000e+00   0.0000
## PctWorkMom                  0.19785   0.000000   0.000000 0.000000e+00   0.0000
## PctKidsBornNeverMar         0.55149   1.000000   1.000000 0.000000e+00   0.0000
## NumImmig                    0.13625   0.000000   0.000000 0.000000e+00   0.0000
## PctImmigRecent              0.15171   0.000000   0.000000 0.000000e+00   0.0000
## PctRecentImmig              0.12426   0.000000   0.000000 0.000000e+00   0.0000
## PctSpeakEnglOnly            0.25162   0.000000   0.000000 1.000000e+00   0.0000
## PctNotSpeakEnglWell         0.09658   0.000000   0.000000 0.000000e+00   0.0000
## PctLargHouseFam             0.36884   0.000000   0.000000 1.000000e+00   1.0000
## PersPerOccupHous            0.27671   0.000000   0.000000 0.000000e+00   0.0000
## PersPerOwnOccHous           0.12975   0.000000   0.000000 0.000000e+00   0.0000
## PersPerRentOccHous          0.12179   1.000000   0.000000 0.000000e+00   0.0000
## PctPersOwnOccup             0.73021   1.000000   1.000000 0.000000e+00   1.0000
## PctPersDenseHous            0.19380   0.000000   0.000000 0.000000e+00   0.0000
## PctHousLess3BR              0.11005   0.000000   0.000000 0.000000e+00   0.0000
## MedNumBR                    0.27777   0.000000   0.000000 0.000000e+00   0.0000
## HousVacant                  0.11109   0.000000   0.000000 1.000000e+00   0.0000
## PctHousOccup                0.43095   0.000000   0.000000 1.000000e+00   0.0000
## PctHousOwnOcc               0.31881   0.000000   0.000000 1.000000e+00   0.0000
## PctVacantBoarded            0.79879   1.000000   1.000000 1.000000e+00   1.0000
## PctVacMore6Mos              0.08111   0.000000   0.000000 0.000000e+00   0.0000
## MedYrHousBuilt              0.31784   0.000000   0.000000 0.000000e+00   0.0000
## PctHousNoPhone              0.99731   1.000000   1.000000 1.000000e+00   1.0000
## PctWOFullPlumb              0.17700   0.000000   0.000000 0.000000e+00   0.0000
## OwnOccLowQuart              0.18149   1.000000   0.000000 1.000000e+00   0.0000
## OwnOccMedVal                0.27885   0.000000   0.000000 0.000000e+00   0.0000
## OwnOccHiQuart               0.60947   0.000000   0.000000 0.000000e+00   1.0000
## RentLowQ                    0.18757   0.000000   0.000000 0.000000e+00   0.0000
## RentMedian                  0.27169   0.000000   0.000000 0.000000e+00   0.0000
## RentHighQ                   0.10597   0.000000   0.000000 0.000000e+00   0.0000
## MedRent                     0.18519   0.000000   0.000000 0.000000e+00   0.0000
## MedRentPctHousInc           0.17910   0.000000   0.000000 0.000000e+00   0.0000
## MedOwnCostPctInc            0.21503   0.000000   1.000000 0.000000e+00   0.0000
## MedOwnCostPctIncNoMtg       0.17921   0.000000   0.000000 0.000000e+00   0.0000
## NumInShelters               0.48236   1.000000   0.000000 0.000000e+00   0.0000
## NumStreet                   0.97218   1.000000   1.000000 1.000000e+00   1.0000
## PctForeignBorn              0.11832   0.000000   0.000000 0.000000e+00   0.0000
## PctBornSameState            0.70002   1.000000   1.000000 1.000000e+00   0.0000
## PctSameHouse85              0.10566   0.000000   0.000000 0.000000e+00   0.0000
## PctSameCity85               0.62188   1.000000   0.000000 1.000000e+00   0.0000
## PctSameState85              0.15228   0.000000   1.000000 0.000000e+00   0.0000
## LandArea                    0.58143   0.000000   1.000000 1.000000e+00   1.0000
## PopDens                     0.87260   1.000000   1.000000 1.000000e+00   0.0000
## PctUsePubTrans              0.11863   0.000000   0.000000 0.000000e+00   0.0000
## LemasPctOfficDrugUn         0.08537   0.000000   0.000000 0.000000e+00   0.0000
## agePct22t29                 0.10488   0.000000   0.000000 0.000000e+00   0.0000
## BF                               NA   0.120061   0.877204 6.091676e-04   1.0000
## PostProbs                        NA   0.000400   0.000400 4.000000e-04   0.0003
## R2                               NA   0.436900   0.436500 4.398000e-01   0.4350
## dim                              NA  20.000000  19.000000 2.400000e+01  18.0000
## logmarg                          NA 487.096306 489.085046 4.818126e+02 489.2161
##                            model 5
## Intercept             1.000000e+00
## population            0.000000e+00
## householdsize         0.000000e+00
## racepctblack          0.000000e+00
## racePctWhite          0.000000e+00
## racePctAsian          0.000000e+00
## racePctHisp           1.000000e+00
## agePct12t29           1.000000e+00
## agePct65up            0.000000e+00
## numbUrban             0.000000e+00
## pctUrban              0.000000e+00
## medIncome             1.000000e+00
## pctWWage              0.000000e+00
## pctWFarmSelf          0.000000e+00
## pctWInvInc            0.000000e+00
## pctWSocSec            1.000000e+00
## pctWPubAsst           0.000000e+00
## pctWRetire            0.000000e+00
## medFamInc             0.000000e+00
## whitePerCap           0.000000e+00
## blackPerCap           0.000000e+00
## indianPerCap          1.000000e+00
## AsianPerCap           0.000000e+00
## OtherPerCap           1.000000e+00
## HispPerCap            0.000000e+00
## NumUnderPov           0.000000e+00
## PctPopUnderPov        0.000000e+00
## PctLess9thGrade       1.000000e+00
## PctBSorMore           1.000000e+00
## PctUnemployed         1.000000e+00
## PctEmploy             0.000000e+00
## PctEmplManu           0.000000e+00
## PctEmplProfServ       0.000000e+00
## PctOccupMgmtProf      0.000000e+00
## MalePctNevMarr        0.000000e+00
## TotalPctDiv           1.000000e+00
## PersPerFam            1.000000e+00
## PctFam2Par            0.000000e+00
## PctWorkMom            0.000000e+00
## PctKidsBornNeverMar   1.000000e+00
## NumImmig              0.000000e+00
## PctImmigRecent        0.000000e+00
## PctRecentImmig        0.000000e+00
## PctSpeakEnglOnly      0.000000e+00
## PctNotSpeakEnglWell   0.000000e+00
## PctLargHouseFam       0.000000e+00
## PersPerOccupHous      0.000000e+00
## PersPerOwnOccHous     0.000000e+00
## PersPerRentOccHous    0.000000e+00
## PctPersOwnOccup       1.000000e+00
## PctPersDenseHous      0.000000e+00
## PctHousLess3BR        0.000000e+00
## MedNumBR              0.000000e+00
## HousVacant            0.000000e+00
## PctHousOccup          1.000000e+00
## PctHousOwnOcc         0.000000e+00
## PctVacantBoarded      0.000000e+00
## PctVacMore6Mos        0.000000e+00
## MedYrHousBuilt        0.000000e+00
## PctHousNoPhone        1.000000e+00
## PctWOFullPlumb        0.000000e+00
## OwnOccLowQuart        0.000000e+00
## OwnOccMedVal          1.000000e+00
## OwnOccHiQuart         0.000000e+00
## RentLowQ              0.000000e+00
## RentMedian            0.000000e+00
## RentHighQ             0.000000e+00
## MedRent               0.000000e+00
## MedRentPctHousInc     1.000000e+00
## MedOwnCostPctInc      1.000000e+00
## MedOwnCostPctIncNoMtg 0.000000e+00
## NumInShelters         0.000000e+00
## NumStreet             1.000000e+00
## PctForeignBorn        0.000000e+00
## PctBornSameState      0.000000e+00
## PctSameHouse85        0.000000e+00
## PctSameCity85         0.000000e+00
## PctSameState85        0.000000e+00
## LandArea              1.000000e+00
## PopDens               1.000000e+00
## PctUsePubTrans        0.000000e+00
## LemasPctOfficDrugUn   0.000000e+00
## agePct22t29           0.000000e+00
## BF                    4.979803e-03
## PostProbs             3.000000e-04
## R2                    4.381000e-01
## dim                   2.200000e+01
## logmarg               4.839137e+02

top 5 model

4.3 Visualization of the Model Space

image(fit.gprior, rotate=F)

4.4 Posterior Distributions of Coefficients

coef.gprior = coef(fit.gprior)
coef.gprior
## 
##  Marginal Posterior Summaries of Coefficients: 
## 
##  Using  BMA 
## 
##  Based on the top  28776 models 
##                        post mean  post SD   post p(B != 0)
## Intercept              36.25610    0.59412   1.00000      
## population             -0.11276    1.01018   0.17079      
## householdsize          -0.11151    0.93677   0.12428      
## racepctblack            0.29775    1.21553   0.18891      
## racePctWhite           -1.59671    2.02059   0.47841      
## racePctAsian           -0.07236    0.47004   0.11505      
## racePctHisp            -3.02083    2.24939   0.73507      
## agePct12t29             1.13897    1.87971   0.35788      
## agePct65up              0.19464    1.16251   0.15857      
## numbUrban              -0.01751    1.00458   0.11212      
## pctUrban                0.22773    1.05728   0.14196      
## medIncome               2.21848    3.65338   0.36661      
## pctWWage               -0.34731    1.26791   0.16627      
## pctWFarmSelf            0.30822    0.64516   0.25505      
## pctWInvInc              0.40781    1.27863   0.16440      
## pctWSocSec              1.00213    1.90600   0.30785      
## pctWPubAsst             0.40263    1.14316   0.17971      
## pctWRetire              0.02619    0.35150   0.09631      
## medFamInc               0.50790    2.33743   0.19363      
## whitePerCap            -0.29561    1.21273   0.13679      
## blackPerCap            -0.17034    0.47447   0.17823      
## indianPerCap           -0.03105    0.19822   0.08147      
## AsianPerCap            -0.04269    0.25657   0.09725      
## OtherPerCap             1.10085    0.91810   0.68301      
## HispPerCap              0.21328    0.59536   0.17658      
## NumUnderPov             0.05197    0.96951   0.13854      
## PctPopUnderPov          0.31834    1.26037   0.15234      
## PctLess9thGrade        -6.69376    1.62698   0.99785      
## PctBSorMore            -0.37315    1.17923   0.17624      
## PctUnemployed           2.29983    1.96959   0.66368      
## PctEmploy              -0.34463    1.11792   0.19160      
## PctEmplManu            -0.09810    0.40049   0.12737      
## PctEmplProfServ        -0.02371    0.40108   0.09685      
## PctOccupMgmtProf       -0.74581    1.48715   0.28694      
## MalePctNevMarr          0.09771    0.73528   0.12311      
## TotalPctDiv             8.19613    1.81851   0.99988      
## PersPerFam              0.98149    2.06481   0.29158      
## PctFam2Par             -0.06169    1.29843   0.11799      
## PctWorkMom             -0.24254    0.63565   0.19785      
## PctKidsBornNeverMar     2.15794    2.30047   0.55149      
## NumImmig                0.15681    0.85698   0.13625      
## PctImmigRecent         -0.13489    0.43956   0.15171      
## PctRecentImmig         -0.14374    0.65267   0.12426      
## PctSpeakEnglOnly        0.86073    1.90558   0.25162      
## PctNotSpeakEnglWell    -0.03239    0.83834   0.09658      
## PctLargHouseFam         1.21245    1.88684   0.36884      
## PersPerOccupHous        1.14790    2.47340   0.27671      
## PersPerOwnOccHous       0.18351    1.14294   0.12975      
## PersPerRentOccHous      0.02096    0.76441   0.12179      
## PctPersOwnOccup        -5.25998    4.40554   0.73021      
## PctPersDenseHous        0.55119    1.52723   0.19380      
## PctHousLess3BR          0.10468    0.67733   0.11005      
## MedNumBR               -0.42230    0.82596   0.27777      
## HousVacant             -0.08871    0.39142   0.11109      
## PctHousOccup           -0.69056    0.95427   0.43095      
## PctHousOwnOcc          -1.08059    3.75318   0.31881      
## PctVacantBoarded        1.91334    1.24028   0.79879      
## PctVacMore6Mos         -0.02101    0.27477   0.08111      
## MedYrHousBuilt         -0.63393    1.13524   0.31784      
## PctHousNoPhone          5.89062    1.41743   0.99731      
## PctWOFullPlumb          0.17295    0.50240   0.17700      
## OwnOccLowQuart         -0.33960    1.86634   0.18149      
## OwnOccMedVal           -1.15216    2.64063   0.27885      
## OwnOccHiQuart          -3.13778    2.98783   0.60947      
## RentLowQ               -0.63935    1.88790   0.18757      
## RentMedian              2.09413    4.70180   0.27169      
## RentHighQ               0.05232    1.03815   0.10597      
## MedRent                -0.92039    3.17173   0.18519      
## MedRentPctHousInc       0.24519    0.66782   0.17910      
## MedOwnCostPctInc       -0.36641    0.88885   0.21503      
## MedOwnCostPctIncNoMtg  -0.19282    0.53333   0.17921      
## NumInShelters           0.93103    1.16441   0.48236      
## NumStreet               2.99064    1.01206   0.97218      
## PctForeignBorn         -0.04504    0.81967   0.11832      
## PctBornSameState       -1.99765    1.64692   0.70002      
## PctSameHouse85          0.07853    0.63592   0.10566      
## PctSameCity85           2.04101    1.92290   0.62188      
## PctSameState85          0.09983    0.75832   0.15228      
## LandArea                1.53476    1.62351   0.58143      
## PopDens                -3.02078    1.57802   0.87260      
## PctUsePubTrans         -0.06793    0.40299   0.11863      
## LemasPctOfficDrugUn     0.01209    0.21032   0.08537      
## agePct22t29            -0.08864    0.51983   0.10488

4.4.1 individual plot

probne0 > 0.2

survivors = which(coef.gprior$probne0 > 0.2)
plot(coef.gprior, subset = survivors, ask = F)

4.4.2 coefficient plot

plot(confint(coef.gprior, parm = survivors))

## NULL

4.5 Prediction

muhat.bma <- fitted(fit.gprior, estimator = "BMA")
bma <- predict(fit.gprior, estimator = "BMA", newdata = data)

result_data = original_data %>%
  mutate(pred_y=bma$fit)
## Warning: Ignoring 208 observations

5 robbbPerPop

y_name = 'robbbPerPop'

5.1 Model fit

f = paste(y_name, " ~ . -murdPerPop -rapesPerPop -robbbPerPop -assaultPerPop -burglPerPop -larcPerPop -autoTheftPerPop -arsonsPerPop")

fit.gprior = bas.lm(f,
                    data = data,
                    method = "MCMC", # better than default "BAS"
                                     # for large p
                   prior = "ZS-null", # default
                                      # "JZS" also can use
                   modelprior = uniform(),
                   include.always = ~1,
                   MCMC.iterations = 100000)
## Warning in bas.lm(f, data = data, method = "MCMC", prior = "ZS-null", modelprior
## = uniform(), : dropping 313 rows due to missing data
plot(fit.gprior, ask = F)

5.2 model result

summary(fit.gprior)
##                       P(B != 0 | Y)     model 1      model 2   model 3
## Intercept                   1.00000    1.000000 1.000000e+00    1.0000
## population                  0.24085    0.000000 1.000000e+00    0.0000
## householdsize               0.13301    1.000000 0.000000e+00    1.0000
## racepctblack                0.99904    1.000000 1.000000e+00    1.0000
## racePctWhite                0.27602    0.000000 0.000000e+00    0.0000
## racePctAsian                0.24028    0.000000 0.000000e+00    0.0000
## racePctHisp                 0.21524    0.000000 1.000000e+00    0.0000
## agePct12t29                 0.34973    0.000000 0.000000e+00    0.0000
## agePct65up                  0.16513    0.000000 1.000000e+00    0.0000
## numbUrban                   0.68399    0.000000 1.000000e+00    1.0000
## pctUrban                    0.32353    1.000000 0.000000e+00    0.0000
## medIncome                   0.29082    0.000000 0.000000e+00    0.0000
## pctWWage                    0.86470    1.000000 0.000000e+00    1.0000
## pctWFarmSelf                0.19030    0.000000 1.000000e+00    0.0000
## pctWInvInc                  0.10909    0.000000 0.000000e+00    0.0000
## pctWSocSec                  0.08138    0.000000 0.000000e+00    0.0000
## pctWPubAsst                 0.14269    0.000000 0.000000e+00    0.0000
## pctWRetire                  0.98991    1.000000 1.000000e+00    1.0000
## medFamInc                   0.09101    0.000000 0.000000e+00    0.0000
## whitePerCap                 0.21822    0.000000 0.000000e+00    0.0000
## blackPerCap                 0.08318    0.000000 0.000000e+00    0.0000
## indianPerCap                0.06973    0.000000 0.000000e+00    0.0000
## AsianPerCap                 0.10215    0.000000 0.000000e+00    0.0000
## OtherPerCap                 0.14922    0.000000 0.000000e+00    0.0000
## HispPerCap                  0.43369    1.000000 1.000000e+00    0.0000
## NumUnderPov                 0.21596    0.000000 0.000000e+00    0.0000
## PctPopUnderPov              0.98912    1.000000 1.000000e+00    1.0000
## PctLess9thGrade             0.99997    1.000000 1.000000e+00    1.0000
## PctBSorMore                 0.78914    1.000000 1.000000e+00    0.0000
## PctUnemployed               0.20705    0.000000 0.000000e+00    1.0000
## PctEmploy                   0.95714    1.000000 1.000000e+00    1.0000
## PctEmplManu                 0.29244    0.000000 0.000000e+00    0.0000
## PctEmplProfServ             0.08015    0.000000 0.000000e+00    0.0000
## PctOccupMgmtProf            0.17435    0.000000 0.000000e+00    0.0000
## MalePctNevMarr              0.99370    1.000000 1.000000e+00    1.0000
## TotalPctDiv                 0.69694    1.000000 1.000000e+00    1.0000
## PersPerFam                  0.77697    1.000000 0.000000e+00    1.0000
## PctFam2Par                  0.08394    0.000000 0.000000e+00    0.0000
## PctWorkMom                  0.99716    1.000000 1.000000e+00    1.0000
## PctKidsBornNeverMar         0.99956    1.000000 1.000000e+00    1.0000
## NumImmig                    0.24117    0.000000 0.000000e+00    0.0000
## PctImmigRecent              0.19211    0.000000 0.000000e+00    0.0000
## PctRecentImmig              0.73653    1.000000 1.000000e+00    1.0000
## PctSpeakEnglOnly            0.15478    0.000000 0.000000e+00    0.0000
## PctNotSpeakEnglWell         0.12281    0.000000 0.000000e+00    0.0000
## PctLargHouseFam             0.12676    0.000000 0.000000e+00    0.0000
## PersPerOccupHous            0.99500    1.000000 1.000000e+00    1.0000
## PersPerOwnOccHous           0.99668    1.000000 1.000000e+00    1.0000
## PersPerRentOccHous          0.99989    1.000000 1.000000e+00    1.0000
## PctPersOwnOccup             0.99900    1.000000 1.000000e+00    1.0000
## PctPersDenseHous            0.99959    1.000000 1.000000e+00    1.0000
## PctHousLess3BR              0.12767    0.000000 0.000000e+00    0.0000
## MedNumBR                    0.05615    0.000000 0.000000e+00    0.0000
## HousVacant                  0.67723    1.000000 1.000000e+00    1.0000
## PctHousOccup                0.09513    0.000000 0.000000e+00    0.0000
## PctHousOwnOcc               0.99914    1.000000 1.000000e+00    1.0000
## PctVacantBoarded            0.99870    1.000000 1.000000e+00    1.0000
## PctVacMore6Mos              0.11004    0.000000 0.000000e+00    0.0000
## MedYrHousBuilt              0.77810    1.000000 0.000000e+00    1.0000
## PctHousNoPhone              0.08553    0.000000 0.000000e+00    0.0000
## PctWOFullPlumb              0.07816    0.000000 0.000000e+00    0.0000
## OwnOccLowQuart              0.12014    0.000000 0.000000e+00    0.0000
## OwnOccMedVal                0.18672    0.000000 0.000000e+00    0.0000
## OwnOccHiQuart               0.82844    1.000000 1.000000e+00    1.0000
## RentLowQ                    0.10712    0.000000 0.000000e+00    0.0000
## RentMedian                  0.09698    0.000000 0.000000e+00    0.0000
## RentHighQ                   0.57972    0.000000 0.000000e+00    0.0000
## MedRent                     0.53887    0.000000 0.000000e+00    0.0000
## MedRentPctHousInc           0.19178    1.000000 0.000000e+00    0.0000
## MedOwnCostPctInc            0.07612    0.000000 0.000000e+00    0.0000
## MedOwnCostPctIncNoMtg       0.99954    1.000000 1.000000e+00    1.0000
## NumInShelters               0.07989    0.000000 0.000000e+00    0.0000
## NumStreet                   0.99969    1.000000 1.000000e+00    1.0000
## PctForeignBorn              0.96635    1.000000 1.000000e+00    1.0000
## PctBornSameState            0.21831    0.000000 0.000000e+00    0.0000
## PctSameHouse85              0.07417    0.000000 0.000000e+00    0.0000
## PctSameCity85               0.07479    0.000000 0.000000e+00    0.0000
## PctSameState85              0.09936    0.000000 0.000000e+00    0.0000
## LandArea                    0.07856    0.000000 0.000000e+00    0.0000
## PopDens                     0.06313    0.000000 0.000000e+00    0.0000
## PctUsePubTrans              0.95855    1.000000 1.000000e+00    1.0000
## LemasPctOfficDrugUn         0.32886    1.000000 0.000000e+00    0.0000
## agePct22t29                 0.99750    1.000000 1.000000e+00    1.0000
## BF                               NA    0.173467 4.292394e-03    1.0000
## PostProbs                        NA    0.000700 6.000000e-04    0.0006
## R2                               NA    0.769100 7.668000e-01    0.7674
## dim                              NA   34.000000 3.200000e+01   31.0000
## logmarg                          NA 1285.111136 1.281412e+03 1286.8629
##                            model 4      model 5
## Intercept             1.000000e+00 1.000000e+00
## population            0.000000e+00 0.000000e+00
## householdsize         0.000000e+00 0.000000e+00
## racepctblack          1.000000e+00 1.000000e+00
## racePctWhite          0.000000e+00 0.000000e+00
## racePctAsian          0.000000e+00 0.000000e+00
## racePctHisp           0.000000e+00 0.000000e+00
## agePct12t29           1.000000e+00 1.000000e+00
## agePct65up            0.000000e+00 0.000000e+00
## numbUrban             0.000000e+00 1.000000e+00
## pctUrban              1.000000e+00 1.000000e+00
## medIncome             0.000000e+00 1.000000e+00
## pctWWage              1.000000e+00 1.000000e+00
## pctWFarmSelf          0.000000e+00 0.000000e+00
## pctWInvInc            0.000000e+00 0.000000e+00
## pctWSocSec            1.000000e+00 0.000000e+00
## pctWPubAsst           0.000000e+00 0.000000e+00
## pctWRetire            1.000000e+00 1.000000e+00
## medFamInc             0.000000e+00 0.000000e+00
## whitePerCap           0.000000e+00 0.000000e+00
## blackPerCap           0.000000e+00 0.000000e+00
## indianPerCap          0.000000e+00 0.000000e+00
## AsianPerCap           0.000000e+00 0.000000e+00
## OtherPerCap           0.000000e+00 0.000000e+00
## HispPerCap            0.000000e+00 0.000000e+00
## NumUnderPov           1.000000e+00 0.000000e+00
## PctPopUnderPov        1.000000e+00 1.000000e+00
## PctLess9thGrade       1.000000e+00 1.000000e+00
## PctBSorMore           1.000000e+00 1.000000e+00
## PctUnemployed         1.000000e+00 0.000000e+00
## PctEmploy             1.000000e+00 1.000000e+00
## PctEmplManu           0.000000e+00 0.000000e+00
## PctEmplProfServ       0.000000e+00 0.000000e+00
## PctOccupMgmtProf      0.000000e+00 0.000000e+00
## MalePctNevMarr        1.000000e+00 1.000000e+00
## TotalPctDiv           1.000000e+00 0.000000e+00
## PersPerFam            1.000000e+00 1.000000e+00
## PctFam2Par            0.000000e+00 0.000000e+00
## PctWorkMom            1.000000e+00 1.000000e+00
## PctKidsBornNeverMar   1.000000e+00 1.000000e+00
## NumImmig              0.000000e+00 0.000000e+00
## PctImmigRecent        0.000000e+00 0.000000e+00
## PctRecentImmig        1.000000e+00 1.000000e+00
## PctSpeakEnglOnly      0.000000e+00 0.000000e+00
## PctNotSpeakEnglWell   0.000000e+00 0.000000e+00
## PctLargHouseFam       0.000000e+00 0.000000e+00
## PersPerOccupHous      1.000000e+00 1.000000e+00
## PersPerOwnOccHous     1.000000e+00 1.000000e+00
## PersPerRentOccHous    1.000000e+00 1.000000e+00
## PctPersOwnOccup       1.000000e+00 1.000000e+00
## PctPersDenseHous      1.000000e+00 1.000000e+00
## PctHousLess3BR        0.000000e+00 0.000000e+00
## MedNumBR              0.000000e+00 0.000000e+00
## HousVacant            0.000000e+00 0.000000e+00
## PctHousOccup          0.000000e+00 0.000000e+00
## PctHousOwnOcc         1.000000e+00 1.000000e+00
## PctVacantBoarded      1.000000e+00 1.000000e+00
## PctVacMore6Mos        0.000000e+00 0.000000e+00
## MedYrHousBuilt        0.000000e+00 1.000000e+00
## PctHousNoPhone        0.000000e+00 0.000000e+00
## PctWOFullPlumb        0.000000e+00 0.000000e+00
## OwnOccLowQuart        0.000000e+00 0.000000e+00
## OwnOccMedVal          0.000000e+00 0.000000e+00
## OwnOccHiQuart         1.000000e+00 1.000000e+00
## RentLowQ              0.000000e+00 0.000000e+00
## RentMedian            0.000000e+00 0.000000e+00
## RentHighQ             0.000000e+00 1.000000e+00
## MedRent               0.000000e+00 1.000000e+00
## MedRentPctHousInc     0.000000e+00 0.000000e+00
## MedOwnCostPctInc      0.000000e+00 0.000000e+00
## MedOwnCostPctIncNoMtg 1.000000e+00 1.000000e+00
## NumInShelters         0.000000e+00 0.000000e+00
## NumStreet             1.000000e+00 1.000000e+00
## PctForeignBorn        1.000000e+00 1.000000e+00
## PctBornSameState      0.000000e+00 1.000000e+00
## PctSameHouse85        0.000000e+00 0.000000e+00
## PctSameCity85         0.000000e+00 0.000000e+00
## PctSameState85        0.000000e+00 0.000000e+00
## LandArea              0.000000e+00 0.000000e+00
## PopDens               0.000000e+00 0.000000e+00
## PctUsePubTrans        1.000000e+00 1.000000e+00
## LemasPctOfficDrugUn   0.000000e+00 0.000000e+00
## agePct22t29           1.000000e+00 1.000000e+00
## BF                    7.292435e-03 3.304046e-02
## PostProbs             6.000000e-04 6.000000e-04
## R2                    7.669000e-01 7.686000e-01
## dim                   3.200000e+01 3.400000e+01
## logmarg               1.281942e+03 1.283453e+03

top 5 model

5.3 Visualization of the Model Space

image(fit.gprior, rotate=F)

5.4 Posterior Distributions of Coefficients

coef.gprior = coef(fit.gprior)
coef.gprior
## 
##  Marginal Posterior Summaries of Coefficients: 
## 
##  Using  BMA 
## 
##  Based on the top  16612 models 
##                        post mean   post SD     post p(B != 0)
## Intercept               166.76597     2.63232     1.00000    
## population                2.66367     5.83202     0.24085    
## householdsize            -1.81116     6.36137     0.13301    
## racepctblack             62.91057    12.84826     0.99904    
## racePctWhite              7.15016    14.47977     0.27602    
## racePctAsian              2.34387     5.24842     0.24028    
## racePctHisp              -3.53246     8.84466     0.21524    
## agePct12t29              -8.04223    12.90874     0.34973    
## agePct65up                2.58321     8.12784     0.16513    
## numbUrban                 9.91987     9.93354     0.68399    
## pctUrban                  1.41901     8.35297     0.32353    
## medIncome                -9.62829    19.15903     0.29082    
## pctWWage                -33.06844    17.56991     0.86470    
## pctWFarmSelf              1.01734     2.59224     0.19030    
## pctWInvInc               -0.94201     4.50484     0.10909    
## pctWSocSec               -0.06230     4.63883     0.08138    
## pctWPubAsst               1.62051     5.27083     0.14269    
## pctWRetire              -20.94698     5.68346     0.98991    
## medFamInc                 0.48294     9.72950     0.09101    
## whitePerCap               4.06247     9.83678     0.21822    
## blackPerCap               0.21111     1.14992     0.08318    
## indianPerCap              0.07367     0.74448     0.06973    
## AsianPerCap               0.29755     1.34663     0.10215    
## OtherPerCap               0.58110     1.79534     0.14922    
## HispPerCap                3.57827     4.78423     0.43369    
## NumUnderPov               2.85408     7.07316     0.21596    
## PctPopUnderPov          -44.83369    12.23251     0.98912    
## PctLess9thGrade         -32.34239     7.32333     0.99997    
## PctBSorMore             -19.35995    13.62785     0.78914    
## PctUnemployed            -2.42446     5.91724     0.20705    
## PctEmploy                38.73775    13.51790     0.95714    
## PctEmplManu              -2.10635     3.88208     0.29244    
## PctEmplProfServ          -0.18482     2.04511     0.08015    
## PctOccupMgmtProf          1.95648     7.61442     0.17435    
## MalePctNevMarr           44.70827    11.39520     0.99370    
## TotalPctDiv              13.70459    11.04227     0.69694    
## PersPerFam              -36.18711    24.88698     0.77697    
## PctFam2Par                0.42748     5.35716     0.08394    
## PctWorkMom              -23.32350     4.99821     0.99716    
## PctKidsBornNeverMar      89.10967     8.35934     0.99956    
## NumImmig                  3.32219     7.34897     0.24117    
## PctImmigRecent           -1.19324     3.03723     0.19211    
## PctRecentImmig          -16.78310    12.33228     0.73653    
## PctSpeakEnglOnly         -2.70058     9.31974     0.15478    
## PctNotSpeakEnglWell       1.68246     6.59471     0.12281    
## PctLargHouseFam           1.58361     6.80657     0.12676    
## PersPerOccupHous       -155.01210    39.28298     0.99500    
## PersPerOwnOccHous       190.08991    27.84114     0.99668    
## PersPerRentOccHous      -71.68713    14.04647     0.99989    
## PctPersOwnOccup        -564.88203    77.20236     0.99900    
## PctPersDenseHous         73.48860    12.20112     0.99959    
## PctHousLess3BR            0.99261     3.95279     0.12767    
## MedNumBR                 -0.01674     0.96318     0.05615    
## HousVacant                6.95871     5.82044     0.67723    
## PctHousOccup             -0.19946     1.30995     0.09513    
## PctHousOwnOcc           562.83647    76.25477     0.99914    
## PctVacantBoarded         23.34907     4.10103     0.99870    
## PctVacMore6Mos           -0.45115     1.84260     0.11004    
## MedYrHousBuilt          -10.33985     7.03420     0.77810    
## PctHousNoPhone           -0.30792     2.31076     0.08553    
## PctWOFullPlumb            0.12180     1.06354     0.07816    
## OwnOccLowQuart           -1.22241     7.13952     0.12014    
## OwnOccMedVal             -3.19720    11.62184     0.18672    
## OwnOccHiQuart           -28.17365    15.79939     0.82844    
## RentLowQ                 -0.99441     4.83726     0.10712    
## RentMedian                1.61968     9.22497     0.09698    
## RentHighQ               -27.89292    28.34398     0.57972    
## MedRent                  24.84778    27.06503     0.53887    
## MedRentPctHousInc         1.31697     3.34885     0.19178    
## MedOwnCostPctInc          0.07004     1.51098     0.07612    
## MedOwnCostPctIncNoMtg   -19.69044     3.75097     0.99954    
## NumInShelters             0.21699     1.40123     0.07989    
## NumStreet                30.63339     4.05005     0.99969    
## PctForeignBorn           48.13008    16.82732     0.96635    
## PctBornSameState         -1.91729     4.59612     0.21831    
## PctSameHouse85           -0.15342     2.34591     0.07417    
## PctSameCity85             0.11067     1.71636     0.07479    
## PctSameState85            0.25618     2.40880     0.09936    
## LandArea                 -0.24390     1.86561     0.07856    
## PopDens                  -0.12720     1.46533     0.06313    
## PctUsePubTrans           14.97322     5.56829     0.95855    
## LemasPctOfficDrugUn       2.15780     3.57912     0.32886    
## agePct22t29             -30.85116     6.92896     0.99750

5.4.1 individual plot

probne0 > 0.2

survivors = which(coef.gprior$probne0 > 0.2)
plot(coef.gprior, subset = survivors, ask = F)

5.4.2 coefficient plot

plot(confint(coef.gprior, parm = survivors))

## NULL

5.5 Prediction

muhat.bma <- fitted(fit.gprior, estimator = "BMA")
bma <- predict(fit.gprior, estimator = "BMA", newdata = data)

result_data = original_data %>%
  mutate(pred_y=bma$fit)
## Warning: Ignoring 1 observations

6 assaultPerPop

y_name = 'assaultPerPop'

6.1 Model fit

f = paste(y_name, " ~ . -murdPerPop -rapesPerPop -robbbPerPop -assaultPerPop -burglPerPop -larcPerPop -autoTheftPerPop -arsonsPerPop")

fit.gprior = bas.lm(f,
                    data = data,
                    method = "MCMC", # better than default "BAS"
                                     # for large p
                   prior = "ZS-null", # default
                                      # "JZS" also can use
                   modelprior = uniform(),
                   include.always = ~1,
                   MCMC.iterations = 100000)
## Warning in bas.lm(f, data = data, method = "MCMC", prior = "ZS-null", modelprior
## = uniform(), : dropping 313 rows due to missing data
plot(fit.gprior, ask = F)

6.2 model result

summary(fit.gprior)
##                       P(B != 0 | Y)   model 1      model 2      model 3
## Intercept                   1.00000   1.00000   1.00000000 1.000000e+00
## population                  0.22884   0.00000   0.00000000 0.000000e+00
## householdsize               0.12883   1.00000   0.00000000 1.000000e+00
## racepctblack                0.69834   0.00000   1.00000000 0.000000e+00
## racePctWhite                0.24563   1.00000   0.00000000 1.000000e+00
## racePctAsian                0.11769   0.00000   0.00000000 0.000000e+00
## racePctHisp                 0.32476   0.00000   1.00000000 0.000000e+00
## agePct12t29                 0.70974   1.00000   1.00000000 1.000000e+00
## agePct65up                  0.11178   0.00000   0.00000000 0.000000e+00
## numbUrban                   0.34357   1.00000   0.00000000 0.000000e+00
## pctUrban                    0.31701   0.00000   1.00000000 1.000000e+00
## medIncome                   0.10371   0.00000   0.00000000 0.000000e+00
## pctWWage                    0.26063   0.00000   0.00000000 0.000000e+00
## pctWFarmSelf                0.10830   0.00000   0.00000000 0.000000e+00
## pctWInvInc                  0.99822   1.00000   1.00000000 1.000000e+00
## pctWSocSec                  0.20756   1.00000   0.00000000 0.000000e+00
## pctWPubAsst                 0.12102   0.00000   0.00000000 0.000000e+00
## pctWRetire                  0.72934   1.00000   1.00000000 0.000000e+00
## medFamInc                   0.11702   0.00000   0.00000000 0.000000e+00
## whitePerCap                 0.10249   0.00000   0.00000000 0.000000e+00
## blackPerCap                 0.09683   0.00000   0.00000000 0.000000e+00
## indianPerCap                0.07663   0.00000   0.00000000 0.000000e+00
## AsianPerCap                 0.38496   1.00000   1.00000000 0.000000e+00
## OtherPerCap                 0.71102   1.00000   1.00000000 0.000000e+00
## HispPerCap                  0.18313   0.00000   0.00000000 1.000000e+00
## NumUnderPov                 0.14849   0.00000   0.00000000 0.000000e+00
## PctPopUnderPov              0.11726   0.00000   0.00000000 0.000000e+00
## PctLess9thGrade             0.10829   0.00000   1.00000000 0.000000e+00
## PctBSorMore                 0.14173   0.00000   0.00000000 0.000000e+00
## PctUnemployed               0.09701   0.00000   0.00000000 0.000000e+00
## PctEmploy                   0.11627   0.00000   0.00000000 0.000000e+00
## PctEmplManu                 0.23949   0.00000   0.00000000 0.000000e+00
## PctEmplProfServ             0.10458   0.00000   0.00000000 0.000000e+00
## PctOccupMgmtProf            0.14689   0.00000   0.00000000 0.000000e+00
## MalePctNevMarr              0.21968   0.00000   0.00000000 0.000000e+00
## TotalPctDiv                 0.16270   0.00000   1.00000000 0.000000e+00
## PersPerFam                  0.12112   0.00000   0.00000000 0.000000e+00
## PctFam2Par                  0.68856   1.00000   1.00000000 1.000000e+00
## PctWorkMom                  0.31405   0.00000   0.00000000 0.000000e+00
## PctKidsBornNeverMar         0.93743   1.00000   1.00000000 1.000000e+00
## NumImmig                    0.52785   0.00000   0.00000000 0.000000e+00
## PctImmigRecent              0.09215   0.00000   0.00000000 0.000000e+00
## PctRecentImmig              0.11802   0.00000   0.00000000 0.000000e+00
## PctSpeakEnglOnly            0.19388   0.00000   0.00000000 0.000000e+00
## PctNotSpeakEnglWell         0.97467   1.00000   1.00000000 1.000000e+00
## PctLargHouseFam             0.11835   0.00000   0.00000000 0.000000e+00
## PersPerOccupHous            0.35375   0.00000   0.00000000 0.000000e+00
## PersPerOwnOccHous           0.67624   1.00000   1.00000000 1.000000e+00
## PersPerRentOccHous          0.29164   0.00000   0.00000000 0.000000e+00
## PctPersOwnOccup             0.32868   0.00000   0.00000000 0.000000e+00
## PctPersDenseHous            0.97769   1.00000   1.00000000 1.000000e+00
## PctHousLess3BR              0.11822   0.00000   0.00000000 0.000000e+00
## MedNumBR                    0.09068   0.00000   0.00000000 0.000000e+00
## HousVacant                  0.08434   0.00000   0.00000000 0.000000e+00
## PctHousOccup                0.90593   1.00000   1.00000000 1.000000e+00
## PctHousOwnOcc               0.33965   0.00000   0.00000000 0.000000e+00
## PctVacantBoarded            0.35965   0.00000   0.00000000 0.000000e+00
## PctVacMore6Mos              0.22355   0.00000   0.00000000 0.000000e+00
## MedYrHousBuilt              0.14705   0.00000   0.00000000 1.000000e+00
## PctHousNoPhone              0.29231   0.00000   0.00000000 1.000000e+00
## PctWOFullPlumb              0.09005   0.00000   0.00000000 0.000000e+00
## OwnOccLowQuart              0.09121   0.00000   0.00000000 0.000000e+00
## OwnOccMedVal                0.09230   0.00000   0.00000000 0.000000e+00
## OwnOccHiQuart               0.09283   0.00000   0.00000000 0.000000e+00
## RentLowQ                    0.83882   1.00000   1.00000000 1.000000e+00
## RentMedian                  0.25138   0.00000   0.00000000 0.000000e+00
## RentHighQ                   0.18862   1.00000   0.00000000 1.000000e+00
## MedRent                     0.53421   0.00000   1.00000000 0.000000e+00
## MedRentPctHousInc           0.09149   0.00000   0.00000000 0.000000e+00
## MedOwnCostPctInc            0.11898   0.00000   0.00000000 0.000000e+00
## MedOwnCostPctIncNoMtg       0.51395   0.00000   1.00000000 0.000000e+00
## NumInShelters               0.14231   0.00000   0.00000000 0.000000e+00
## NumStreet                   0.99944   1.00000   1.00000000 1.000000e+00
## PctForeignBorn              0.19998   0.00000   1.00000000 0.000000e+00
## PctBornSameState            0.11822   0.00000   0.00000000 0.000000e+00
## PctSameHouse85              0.14555   0.00000   0.00000000 0.000000e+00
## PctSameCity85               0.15789   0.00000   0.00000000 0.000000e+00
## PctSameState85              0.11912   0.00000   0.00000000 0.000000e+00
## LandArea                    0.14014   0.00000   0.00000000 0.000000e+00
## PopDens                     0.54734   1.00000   1.00000000 1.000000e+00
## PctUsePubTrans              0.20710   0.00000   0.00000000 0.000000e+00
## LemasPctOfficDrugUn         0.09826   0.00000   0.00000000 0.000000e+00
## agePct22t29                 0.20048   0.00000   0.00000000 0.000000e+00
## BF                               NA   0.11119   0.04132928 2.758002e-03
## PostProbs                        NA   0.00050   0.00040000 4.000000e-04
## R2                               NA   0.49250   0.49620000 4.891000e-01
## dim                              NA  20.00000  23.00000000 1.900000e+01
## logmarg                          NA 584.94858 583.95890954 5.812518e+02
##                            model 4  model 5
## Intercept             1.000000e+00   1.0000
## population            0.000000e+00   0.0000
## householdsize         0.000000e+00   0.0000
## racepctblack          1.000000e+00   1.0000
## racePctWhite          0.000000e+00   0.0000
## racePctAsian          0.000000e+00   0.0000
## racePctHisp           1.000000e+00   0.0000
## agePct12t29           1.000000e+00   1.0000
## agePct65up            0.000000e+00   0.0000
## numbUrban             0.000000e+00   0.0000
## pctUrban              1.000000e+00   1.0000
## medIncome             0.000000e+00   0.0000
## pctWWage              0.000000e+00   0.0000
## pctWFarmSelf          0.000000e+00   0.0000
## pctWInvInc            1.000000e+00   1.0000
## pctWSocSec            1.000000e+00   0.0000
## pctWPubAsst           1.000000e+00   0.0000
## pctWRetire            1.000000e+00   1.0000
## medFamInc             1.000000e+00   0.0000
## whitePerCap           0.000000e+00   0.0000
## blackPerCap           0.000000e+00   0.0000
## indianPerCap          0.000000e+00   0.0000
## AsianPerCap           1.000000e+00   1.0000
## OtherPerCap           1.000000e+00   1.0000
## HispPerCap            0.000000e+00   0.0000
## NumUnderPov           1.000000e+00   0.0000
## PctPopUnderPov        0.000000e+00   0.0000
## PctLess9thGrade       0.000000e+00   0.0000
## PctBSorMore           0.000000e+00   0.0000
## PctUnemployed         0.000000e+00   0.0000
## PctEmploy             0.000000e+00   0.0000
## PctEmplManu           0.000000e+00   0.0000
## PctEmplProfServ       0.000000e+00   0.0000
## PctOccupMgmtProf      0.000000e+00   0.0000
## MalePctNevMarr        1.000000e+00   0.0000
## TotalPctDiv           0.000000e+00   0.0000
## PersPerFam            0.000000e+00   0.0000
## PctFam2Par            1.000000e+00   1.0000
## PctWorkMom            0.000000e+00   1.0000
## PctKidsBornNeverMar   1.000000e+00   1.0000
## NumImmig              1.000000e+00   0.0000
## PctImmigRecent        0.000000e+00   0.0000
## PctRecentImmig        0.000000e+00   0.0000
## PctSpeakEnglOnly      0.000000e+00   1.0000
## PctNotSpeakEnglWell   1.000000e+00   1.0000
## PctLargHouseFam       0.000000e+00   0.0000
## PersPerOccupHous      0.000000e+00   0.0000
## PersPerOwnOccHous     0.000000e+00   1.0000
## PersPerRentOccHous    1.000000e+00   0.0000
## PctPersOwnOccup       1.000000e+00   0.0000
## PctPersDenseHous      1.000000e+00   1.0000
## PctHousLess3BR        0.000000e+00   0.0000
## MedNumBR              0.000000e+00   0.0000
## HousVacant            0.000000e+00   0.0000
## PctHousOccup          1.000000e+00   1.0000
## PctHousOwnOcc         1.000000e+00   0.0000
## PctVacantBoarded      0.000000e+00   1.0000
## PctVacMore6Mos        0.000000e+00   0.0000
## MedYrHousBuilt        0.000000e+00   0.0000
## PctHousNoPhone        0.000000e+00   0.0000
## PctWOFullPlumb        0.000000e+00   0.0000
## OwnOccLowQuart        0.000000e+00   0.0000
## OwnOccMedVal          0.000000e+00   0.0000
## OwnOccHiQuart         0.000000e+00   0.0000
## RentLowQ              1.000000e+00   1.0000
## RentMedian            1.000000e+00   0.0000
## RentHighQ             0.000000e+00   0.0000
## MedRent               0.000000e+00   1.0000
## MedRentPctHousInc     0.000000e+00   0.0000
## MedOwnCostPctInc      0.000000e+00   0.0000
## MedOwnCostPctIncNoMtg 0.000000e+00   1.0000
## NumInShelters         1.000000e+00   0.0000
## NumStreet             1.000000e+00   1.0000
## PctForeignBorn        0.000000e+00   0.0000
## PctBornSameState      0.000000e+00   0.0000
## PctSameHouse85        0.000000e+00   0.0000
## PctSameCity85         0.000000e+00   0.0000
## PctSameState85        0.000000e+00   0.0000
## LandArea              0.000000e+00   0.0000
## PopDens               0.000000e+00   1.0000
## PctUsePubTrans        1.000000e+00   0.0000
## LemasPctOfficDrugUn   0.000000e+00   0.0000
## agePct22t29           1.000000e+00   0.0000
## BF                    4.544706e-07   1.0000
## PostProbs             4.000000e-04   0.0004
## R2                    4.982000e-01   0.4965
## dim                   2.900000e+01  22.0000
## logmarg               5.725410e+02 587.1451

top 5 model

6.3 Visualization of the Model Space

image(fit.gprior, rotate=F)

6.4 Posterior Distributions of Coefficients

coef.gprior = coef(fit.gprior)
coef.gprior
## 
##  Marginal Posterior Summaries of Coefficients: 
## 
##  Using  BMA 
## 
##  Based on the top  27177 models 
##                        post mean  post SD    post p(B != 0)
## Intercept              374.70427    6.68862    1.00000     
## population              -7.20662   18.63811    0.22884     
## householdsize            0.55810    9.85411    0.12883     
## racepctblack            32.76431   26.49645    0.69834     
## racePctWhite            -8.12580   19.42643    0.24563     
## racePctAsian            -0.80993    4.77867    0.11769     
## racePctHisp             12.41428   21.44071    0.32476     
## agePct12t29            -29.75835   26.55547    0.70974     
## agePct65up               1.29601   10.06931    0.11178     
## numbUrban                6.49990   13.23122    0.34357     
## pctUrban                 6.23957   12.51196    0.31701     
## medIncome                2.81504   14.59791    0.10371     
## pctWWage                -9.25242   19.79404    0.26063     
## pctWFarmSelf             0.41148    3.14187    0.10830     
## pctWInvInc             -85.02458   22.96546    0.99822     
## pctWSocSec               6.37727   16.56620    0.20756     
## pctWPubAsst              1.95133    8.78632    0.12102     
## pctWRetire             -21.47679   16.60236    0.72934     
## medFamInc                1.72536   12.74148    0.11702     
## whitePerCap              0.23487    7.67170    0.10249     
## blackPerCap             -0.67872    3.21487    0.09683     
## indianPerCap            -0.13600    1.89588    0.07663     
## AsianPerCap              6.04234    9.09630    0.38496     
## OtherPerCap             13.67158   10.62906    0.71102     
## HispPerCap               2.47788    6.80861    0.18313     
## NumUnderPov             -1.66370   13.92155    0.14849     
## PctPopUnderPov          -0.50972   10.31127    0.11726     
## PctLess9thGrade          1.42960    7.68080    0.10829     
## PctBSorMore              2.40462   10.47981    0.14173     
## PctUnemployed           -0.97078    5.98649    0.09701     
## PctEmploy               -0.07083    8.45118    0.11627     
## PctEmplManu             -3.48227    7.64211    0.23949     
## PctEmplProfServ         -0.54026    4.91836    0.10458     
## PctOccupMgmtProf         3.23855   11.02576    0.14689     
## MalePctNevMarr           5.46315   18.56939    0.21968     
## TotalPctDiv             -0.73925   11.81192    0.16270     
## PersPerFam               2.85376   16.44289    0.12112     
## PctFam2Par             -52.00146   44.07666    0.68856     
## PctWorkMom              -5.59939    9.96053    0.31405     
## PctKidsBornNeverMar     76.51008   32.02011    0.93743     
## NumImmig                24.37726   29.54705    0.52785     
## PctImmigRecent          -0.28782    2.94373    0.09215     
## PctRecentImmig          -1.87663    8.77889    0.11802     
## PctSpeakEnglOnly        -5.23182   16.98263    0.19388     
## PctNotSpeakEnglWell    -86.80345   31.44144    0.97467     
## PctLargHouseFam         -2.13334   10.65830    0.11835     
## PersPerOccupHous        27.68085   51.42329    0.35375     
## PersPerOwnOccHous      -47.27123   44.60627    0.67624     
## PersPerRentOccHous     -15.02904   29.85264    0.29164     
## PctPersOwnOccup        -76.48118  140.21452    0.32868     
## PctPersDenseHous        93.27523   29.81227    0.97769     
## PctHousLess3BR           1.96796    9.01438    0.11822     
## MedNumBR                -0.49485    3.44420    0.09068     
## HousVacant              -0.41956    3.18511    0.08434     
## PctHousOccup           -24.26747   11.58629    0.90593     
## PctHousOwnOcc           69.43228  130.47776    0.33965     
## PctVacantBoarded         6.91463   11.00599    0.35965     
## PctVacMore6Mos          -3.61813    8.32075    0.22355     
## MedYrHousBuilt           2.09065    7.31535    0.14705     
## PctHousNoPhone           8.38583   15.60851    0.29231     
## PctWOFullPlumb          -0.53629    3.20824    0.09005     
## OwnOccLowQuart           0.91189    8.21787    0.09121     
## OwnOccMedVal             0.37935    8.66237    0.09230     
## OwnOccHiQuart            0.23307    7.01888    0.09283     
## RentLowQ               -71.25901   41.58933    0.83882     
## RentMedian              19.02320   42.56626    0.25138     
## RentHighQ                8.92775   24.85031    0.18862     
## MedRent                 47.34124   51.54773    0.53421     
## MedRentPctHousInc       -0.12809    3.32187    0.09149     
## MedOwnCostPctInc        -1.42727    5.87969    0.11898     
## MedOwnCostPctIncNoMtg  -10.71670   12.43469    0.51395     
## NumInShelters            1.47406    5.41465    0.14231     
## NumStreet               44.00144    9.71786    0.99944     
## PctForeignBorn           6.78644   19.38718    0.19998     
## PctBornSameState         0.59927    4.54076    0.11822     
## PctSameHouse85           2.42145    8.85619    0.14555     
## PctSameCity85            2.54845    8.24808    0.15789     
## PctSameState85           1.08798    4.88852    0.11912     
## LandArea                 1.43458    6.92917    0.14014     
## PopDens                -13.85212   14.99277    0.54734     
## PctUsePubTrans          -3.32780    8.24665    0.20710     
## LemasPctOfficDrugUn      0.60801    3.10082    0.09826     
## agePct22t29             -4.19196   11.14075    0.20048

6.4.1 individual plot

probne0 > 0.2

survivors = which(coef.gprior$probne0 > 0.2)
plot(coef.gprior, subset = survivors, ask = F)

6.4.2 coefficient plot

plot(confint(coef.gprior, parm = survivors))

## NULL

6.5 Prediction

muhat.bma <- fitted(fit.gprior, estimator = "BMA")
bma <- predict(fit.gprior, estimator = "BMA", newdata = data)

result_data = original_data %>%
  mutate(pred_y=bma$fit)
## Warning: Ignoring 13 observations

7 burglPerPop

y_name = 'burglPerPop'

7.1 Model fit

f = paste(y_name, " ~ . -murdPerPop -rapesPerPop -robbbPerPop -assaultPerPop -burglPerPop -larcPerPop -autoTheftPerPop -arsonsPerPop")

fit.gprior = bas.lm(f,
                    data = data,
                    method = "MCMC", # better than default "BAS"
                                     # for large p
                   prior = "ZS-null", # default
                                      # "JZS" also can use
                   modelprior = uniform(),
                   include.always = ~1,
                   MCMC.iterations = 100000)
## Warning in bas.lm(f, data = data, method = "MCMC", prior = "ZS-null", modelprior
## = uniform(), : dropping 313 rows due to missing data
plot(fit.gprior, ask = F)

7.2 model result

summary(fit.gprior)
##                       P(B != 0 | Y)      model 1      model 2      model 3
## Intercept                   1.00000   1.00000000 1.000000e+00   1.00000000
## population                  0.18091   0.00000000 1.000000e+00   1.00000000
## householdsize               0.89274   1.00000000 0.000000e+00   1.00000000
## racepctblack                0.96108   1.00000000 1.000000e+00   1.00000000
## racePctWhite                0.09902   0.00000000 0.000000e+00   0.00000000
## racePctAsian                0.10389   0.00000000 0.000000e+00   0.00000000
## racePctHisp                 0.14769   0.00000000 0.000000e+00   0.00000000
## agePct12t29                 0.28871   0.00000000 0.000000e+00   0.00000000
## agePct65up                  0.16634   0.00000000 0.000000e+00   0.00000000
## numbUrban                   0.35407   1.00000000 0.000000e+00   0.00000000
## pctUrban                    0.49945   0.00000000 0.000000e+00   0.00000000
## medIncome                   0.09063   0.00000000 0.000000e+00   0.00000000
## pctWWage                    0.12374   0.00000000 0.000000e+00   0.00000000
## pctWFarmSelf                0.07145   0.00000000 0.000000e+00   0.00000000
## pctWInvInc                  0.46062   0.00000000 0.000000e+00   0.00000000
## pctWSocSec                  0.87530   1.00000000 1.000000e+00   1.00000000
## pctWPubAsst                 0.46020   1.00000000 0.000000e+00   1.00000000
## pctWRetire                  0.98374   1.00000000 1.000000e+00   1.00000000
## medFamInc                   0.11418   0.00000000 0.000000e+00   0.00000000
## whitePerCap                 0.99026   1.00000000 1.000000e+00   1.00000000
## blackPerCap                 0.08740   0.00000000 0.000000e+00   0.00000000
## indianPerCap                0.09180   0.00000000 0.000000e+00   0.00000000
## AsianPerCap                 0.07523   0.00000000 0.000000e+00   0.00000000
## OtherPerCap                 0.28600   0.00000000 1.000000e+00   0.00000000
## HispPerCap                  0.11045   0.00000000 0.000000e+00   0.00000000
## NumUnderPov                 0.15994   0.00000000 0.000000e+00   0.00000000
## PctPopUnderPov              0.13281   0.00000000 1.000000e+00   0.00000000
## PctLess9thGrade             0.70854   1.00000000 0.000000e+00   1.00000000
## PctBSorMore                 0.13210   0.00000000 1.000000e+00   0.00000000
## PctUnemployed               0.09563   1.00000000 0.000000e+00   0.00000000
## PctEmploy                   0.39009   0.00000000 1.000000e+00   1.00000000
## PctEmplManu                 0.20842   0.00000000 0.000000e+00   0.00000000
## PctEmplProfServ             0.09711   0.00000000 0.000000e+00   0.00000000
## PctOccupMgmtProf            0.39280   0.00000000 1.000000e+00   0.00000000
## MalePctNevMarr              0.99244   1.00000000 1.000000e+00   1.00000000
## TotalPctDiv                 0.97465   1.00000000 1.000000e+00   1.00000000
## PersPerFam                  0.20855   0.00000000 0.000000e+00   0.00000000
## PctFam2Par                  0.30995   0.00000000 1.000000e+00   0.00000000
## PctWorkMom                  0.29563   0.00000000 1.000000e+00   1.00000000
## PctKidsBornNeverMar         0.61733   1.00000000 0.000000e+00   1.00000000
## NumImmig                    0.70538   0.00000000 1.000000e+00   1.00000000
## PctImmigRecent              0.11919   0.00000000 0.000000e+00   0.00000000
## PctRecentImmig              0.79777   1.00000000 0.000000e+00   1.00000000
## PctSpeakEnglOnly            0.26757   0.00000000 0.000000e+00   0.00000000
## PctNotSpeakEnglWell         0.14905   0.00000000 0.000000e+00   0.00000000
## PctLargHouseFam             0.13885   0.00000000 1.000000e+00   0.00000000
## PersPerOccupHous            0.92578   1.00000000 0.000000e+00   1.00000000
## PersPerOwnOccHous           0.62694   0.00000000 0.000000e+00   0.00000000
## PersPerRentOccHous          0.30072   0.00000000 0.000000e+00   0.00000000
## PctPersOwnOccup             0.49837   1.00000000 1.000000e+00   1.00000000
## PctPersDenseHous            0.35755   0.00000000 0.000000e+00   0.00000000
## PctHousLess3BR              0.10954   0.00000000 0.000000e+00   1.00000000
## MedNumBR                    0.16149   0.00000000 0.000000e+00   0.00000000
## HousVacant                  0.43073   0.00000000 0.000000e+00   1.00000000
## PctHousOccup                0.99917   1.00000000 1.000000e+00   1.00000000
## PctHousOwnOcc               0.49741   1.00000000 1.000000e+00   1.00000000
## PctVacantBoarded            0.17623   0.00000000 0.000000e+00   0.00000000
## PctVacMore6Mos              0.89907   0.00000000 1.000000e+00   1.00000000
## MedYrHousBuilt              0.15693   0.00000000 0.000000e+00   0.00000000
## PctHousNoPhone              0.73584   1.00000000 0.000000e+00   1.00000000
## PctWOFullPlumb              0.07007   0.00000000 0.000000e+00   0.00000000
## OwnOccLowQuart              0.12070   0.00000000 0.000000e+00   0.00000000
## OwnOccMedVal                0.12010   0.00000000 0.000000e+00   0.00000000
## OwnOccHiQuart               0.34339   1.00000000 0.000000e+00   0.00000000
## RentLowQ                    0.60429   0.00000000 1.000000e+00   0.00000000
## RentMedian                  0.14430   1.00000000 0.000000e+00   0.00000000
## RentHighQ                   0.84994   0.00000000 1.000000e+00   1.00000000
## MedRent                     0.42824   0.00000000 1.000000e+00   0.00000000
## MedRentPctHousInc           0.85814   1.00000000 1.000000e+00   1.00000000
## MedOwnCostPctInc            0.08788   0.00000000 0.000000e+00   0.00000000
## MedOwnCostPctIncNoMtg       0.08498   0.00000000 1.000000e+00   0.00000000
## NumInShelters               0.10264   0.00000000 1.000000e+00   0.00000000
## NumStreet                   0.97489   1.00000000 1.000000e+00   1.00000000
## PctForeignBorn              0.77244   1.00000000 0.000000e+00   1.00000000
## PctBornSameState            0.13626   0.00000000 0.000000e+00   0.00000000
## PctSameHouse85              0.20324   1.00000000 0.000000e+00   0.00000000
## PctSameCity85               0.12435   0.00000000 0.000000e+00   0.00000000
## PctSameState85              0.09740   0.00000000 0.000000e+00   0.00000000
## LandArea                    0.12276   0.00000000 0.000000e+00   0.00000000
## PopDens                     0.57622   1.00000000 0.000000e+00   0.00000000
## PctUsePubTrans              0.80152   1.00000000 1.000000e+00   1.00000000
## LemasPctOfficDrugUn         0.08598   0.00000000 0.000000e+00   0.00000000
## agePct22t29                 0.20962   0.00000000 0.000000e+00   0.00000000
## BF                               NA   0.03618418 6.127948e-05   0.03385791
## PostProbs                        NA   0.00060000 6.000000e-04   0.00050000
## R2                               NA   0.56530000 5.647000e-01   0.56770000
## dim                              NA  27.00000000 2.900000e+01  29.00000000
## logmarg                          NA 712.17299899 7.057921e+02 712.10654953
##                        model 4     model 5
## Intercept               1.0000   1.0000000
## population              0.0000   0.0000000
## householdsize           1.0000   1.0000000
## racepctblack            1.0000   1.0000000
## racePctWhite            0.0000   0.0000000
## racePctAsian            0.0000   0.0000000
## racePctHisp             0.0000   0.0000000
## agePct12t29             1.0000   0.0000000
## agePct65up              0.0000   0.0000000
## numbUrban               0.0000   0.0000000
## pctUrban                1.0000   0.0000000
## medIncome               0.0000   0.0000000
## pctWWage                0.0000   0.0000000
## pctWFarmSelf            0.0000   0.0000000
## pctWInvInc              0.0000   1.0000000
## pctWSocSec              1.0000   1.0000000
## pctWPubAsst             1.0000   0.0000000
## pctWRetire              1.0000   1.0000000
## medFamInc               0.0000   0.0000000
## whitePerCap             1.0000   1.0000000
## blackPerCap             0.0000   0.0000000
## indianPerCap            0.0000   0.0000000
## AsianPerCap             0.0000   0.0000000
## OtherPerCap             0.0000   0.0000000
## HispPerCap              0.0000   0.0000000
## NumUnderPov             0.0000   0.0000000
## PctPopUnderPov          0.0000   1.0000000
## PctLess9thGrade         1.0000   1.0000000
## PctBSorMore             0.0000   0.0000000
## PctUnemployed           0.0000   0.0000000
## PctEmploy               0.0000   0.0000000
## PctEmplManu             0.0000   0.0000000
## PctEmplProfServ         0.0000   0.0000000
## PctOccupMgmtProf        0.0000   1.0000000
## MalePctNevMarr          1.0000   1.0000000
## TotalPctDiv             1.0000   1.0000000
## PersPerFam              0.0000   0.0000000
## PctFam2Par              0.0000   0.0000000
## PctWorkMom              0.0000   0.0000000
## PctKidsBornNeverMar     1.0000   1.0000000
## NumImmig                1.0000   1.0000000
## PctImmigRecent          0.0000   0.0000000
## PctRecentImmig          1.0000   1.0000000
## PctSpeakEnglOnly        0.0000   0.0000000
## PctNotSpeakEnglWell     0.0000   0.0000000
## PctLargHouseFam         0.0000   0.0000000
## PersPerOccupHous        1.0000   1.0000000
## PersPerOwnOccHous       0.0000   1.0000000
## PersPerRentOccHous      0.0000   0.0000000
## PctPersOwnOccup         1.0000   0.0000000
## PctPersDenseHous        0.0000   1.0000000
## PctHousLess3BR          0.0000   0.0000000
## MedNumBR                0.0000   0.0000000
## HousVacant              1.0000   1.0000000
## PctHousOccup            1.0000   1.0000000
## PctHousOwnOcc           1.0000   0.0000000
## PctVacantBoarded        0.0000   0.0000000
## PctVacMore6Mos          1.0000   1.0000000
## MedYrHousBuilt          0.0000   0.0000000
## PctHousNoPhone          1.0000   1.0000000
## PctWOFullPlumb          0.0000   0.0000000
## OwnOccLowQuart          1.0000   0.0000000
## OwnOccMedVal            0.0000   0.0000000
## OwnOccHiQuart           0.0000   0.0000000
## RentLowQ                0.0000   0.0000000
## RentMedian              0.0000   0.0000000
## RentHighQ               1.0000   1.0000000
## MedRent                 0.0000   0.0000000
## MedRentPctHousInc       1.0000   1.0000000
## MedOwnCostPctInc        0.0000   0.0000000
## MedOwnCostPctIncNoMtg   0.0000   0.0000000
## NumInShelters           0.0000   0.0000000
## NumStreet               1.0000   1.0000000
## PctForeignBorn          1.0000   1.0000000
## PctBornSameState        0.0000   0.0000000
## PctSameHouse85          0.0000   0.0000000
## PctSameCity85           0.0000   0.0000000
## PctSameState85          0.0000   0.0000000
## LandArea                0.0000   0.0000000
## PopDens                 1.0000   1.0000000
## PctUsePubTrans          0.0000   0.0000000
## LemasPctOfficDrugUn     0.0000   0.0000000
## agePct22t29             0.0000   1.0000000
## BF                      1.0000   0.1858539
## PostProbs               0.0005   0.0005000
## R2                      0.5681   0.5673000
## dim                    28.0000  28.0000000
## logmarg               715.4921 713.8093380

top 5 model

7.3 Visualization of the Model Space

image(fit.gprior, rotate=F)

7.4 Posterior Distributions of Coefficients

coef.gprior = coef(fit.gprior)

coef.gprior
## 
##  Marginal Posterior Summaries of Coefficients: 
## 
##  Using  BMA 
## 
##  Based on the top  22804 models 
##                        post mean   post SD     post p(B != 0)
## Intercept              1056.78964    11.81393     1.00000    
## population               -9.26887    32.53918     0.18091    
## householdsize          -153.53673    70.82293     0.89274    
## racepctblack            111.75688    41.84016     0.96108    
## racePctWhite              0.45568    20.58773     0.09902    
## racePctAsian              1.28270     8.07831     0.10389    
## racePctHisp               4.71611    19.91023     0.14769    
## agePct12t29             -27.67509    53.94940     0.28871    
## agePct65up               10.67873    41.63702     0.16634    
## numbUrban                10.66069    32.45154     0.35407    
## pctUrban                 24.01983    33.58814     0.49945    
## medIncome                -1.08704    31.48142     0.09063    
## pctWWage                 -6.79032    32.93527     0.12374    
## pctWFarmSelf              0.33706     4.26528     0.07145    
## pctWInvInc              -44.23767    57.46525     0.46062    
## pctWSocSec              134.10971    68.16002     0.87530    
## pctWPubAsst              34.79750    44.43794     0.46020    
## pctWRetire              -86.16907    25.70903     0.98374    
## medFamInc                -6.78459    37.71428     0.11418    
## whitePerCap             152.02366    47.28795     0.99026    
## blackPerCap               0.16634     4.18880     0.08740    
## indianPerCap             -0.33078     3.71771     0.09180    
## AsianPerCap               0.20321     3.96404     0.07523    
## OtherPerCap               6.70692    12.61263     0.28600    
## HispPerCap                0.79298     6.33354     0.11045    
## NumUnderPov               4.01050    30.84169     0.15994    
## PctPopUnderPov            7.11240    31.09752     0.13281    
## PctLess9thGrade         -65.81723    52.07354     0.70854    
## PctBSorMore              -6.82790    30.74429     0.13210    
## PctUnemployed            -1.21354    10.99369     0.09563    
## PctEmploy                37.02491    56.99253     0.39009    
## PctEmplManu              -5.38577    13.29282     0.20842    
## PctEmplProfServ          -1.17247     9.54212     0.09711    
## PctOccupMgmtProf         31.00061    48.20641     0.39280    
## MalePctNevMarr          189.56181    49.92505     0.99244    
## TotalPctDiv             178.70027    52.13048     0.97465    
## PersPerFam              -21.52295    54.13092     0.20855    
## PctFam2Par              -36.66774    69.59367     0.30995    
## PctWorkMom              -11.36836    22.11326     0.29563    
## PctKidsBornNeverMar      56.56951    53.67053     0.61733    
## NumImmig                 68.66892    59.03795     0.70538    
## PctImmigRecent           -1.59372     8.45610     0.11919    
## PctRecentImmig          -90.06808    58.22858     0.79777    
## PctSpeakEnglOnly        -21.48534    44.02267     0.26757    
## PctNotSpeakEnglWell      -8.54371    31.98522     0.14905    
## PctLargHouseFam          -4.61786    22.45401     0.13885    
## PersPerOccupHous        385.85465   189.35321     0.92578    
## PersPerOwnOccHous      -127.65396   127.38742     0.62694    
## PersPerRentOccHous      -30.96579    60.59847     0.30072    
## PctPersOwnOccup        -289.75697   369.38546     0.49837    
## PctPersDenseHous        -30.74458    50.38828     0.35755    
## PctHousLess3BR            3.38597    15.73736     0.10954    
## MedNumBR                 -3.73499    11.20557     0.16149    
## HousVacant              -16.18250    22.09768     0.43073    
## PctHousOccup           -101.49069    17.92150     0.99917    
## PctHousOwnOcc           301.69785   370.88730     0.49741    
## PctVacantBoarded          4.96729    13.29818     0.17623    
## PctVacMore6Mos          -47.00927    22.75144     0.89907    
## MedYrHousBuilt            4.39576    14.18112     0.15693    
## PctHousNoPhone           59.48536    44.56622     0.73584    
## PctWOFullPlumb           -0.09972     4.26226     0.07007    
## OwnOccLowQuart           -3.98060    22.88371     0.12070    
## OwnOccMedVal             -3.49519    28.51354     0.12010    
## OwnOccHiQuart           -27.94096    47.65853     0.34339    
## RentLowQ                -69.76059    69.52005     0.60429    
## RentMedian               -5.79381    50.62850     0.14430    
## RentHighQ              -177.09073   106.88745     0.84994    
## MedRent                  79.19881   111.20196     0.42824    
## MedRentPctHousInc        51.50432    28.41898     0.85814    
## MedOwnCostPctInc          1.17200     8.23629     0.08788    
## MedOwnCostPctIncNoMtg     0.40438     5.28809     0.08498    
## NumInShelters             0.67475     6.56027     0.10264    
## NumStreet                61.23972    20.02747     0.97489    
## PctForeignBorn          135.01400    92.69097     0.77244    
## PctBornSameState         -3.20281    11.84018     0.13626    
## PctSameHouse85           -9.05832    23.04565     0.20324    
## PctSameCity85            -2.74580    11.90818     0.12435    
## PctSameState85           -1.26656     7.95114     0.09740    
## LandArea                  1.92571    10.85746     0.12276    
## PopDens                 -31.11407    31.95691     0.57622    
## PctUsePubTrans          -45.83716    29.57892     0.80152    
## LemasPctOfficDrugUn       0.07110     4.16807     0.08598    
## agePct22t29              -8.46298    21.23919     0.20962

7.4.1 individual plot

probne0 > 0.2

survivors = which(coef.gprior$probne0 > 0.2)
plot(coef.gprior, subset = survivors, ask = F)

7.4.2 coefficient plot

plot(confint(coef.gprior, parm = survivors))

## NULL

7.5 Prediction

muhat.bma <- fitted(fit.gprior, estimator = "BMA")
bma <- predict(fit.gprior, estimator = "BMA", newdata = data)

result_data = original_data %>%
  mutate(pred_y=bma$fit)
## Warning: Ignoring 3 observations

8 larcPerPop

y_name = 'larcPerPop'

8.1 Model fit

f = paste(y_name, " ~ . -murdPerPop -rapesPerPop -robbbPerPop -assaultPerPop -burglPerPop -larcPerPop -autoTheftPerPop -arsonsPerPop")

fit.gprior = bas.lm(f,
                    data = data,
                    method = "MCMC", # better than default "BAS"
                                     # for large p
                   prior = "ZS-null", # default
                                      # "JZS" also can use
                   modelprior = uniform(),
                   include.always = ~1,
                   MCMC.iterations = 100000)
## Warning in bas.lm(f, data = data, method = "MCMC", prior = "ZS-null", modelprior
## = uniform(), : dropping 313 rows due to missing data
plot(fit.gprior, ask = F)

8.2 model result

summary(fit.gprior)
##                       P(B != 0 | Y)      model 1      model 2      model 3
## Intercept                   1.00000 1.000000e+00 1.000000e+00   1.00000000
## population                  0.18555 0.000000e+00 0.000000e+00   1.00000000
## householdsize               0.23120 1.000000e+00 0.000000e+00   0.00000000
## racepctblack                0.16173 0.000000e+00 0.000000e+00   0.00000000
## racePctWhite                0.12005 0.000000e+00 0.000000e+00   0.00000000
## racePctAsian                0.15541 0.000000e+00 0.000000e+00   0.00000000
## racePctHisp                 0.14863 0.000000e+00 1.000000e+00   0.00000000
## agePct12t29                 0.39296 1.000000e+00 1.000000e+00   0.00000000
## agePct65up                  0.32464 0.000000e+00 0.000000e+00   0.00000000
## numbUrban                   0.11884 0.000000e+00 0.000000e+00   0.00000000
## pctUrban                    0.13001 0.000000e+00 0.000000e+00   0.00000000
## medIncome                   0.23166 0.000000e+00 0.000000e+00   0.00000000
## pctWWage                    0.68194 1.000000e+00 0.000000e+00   1.00000000
## pctWFarmSelf                0.16497 0.000000e+00 1.000000e+00   0.00000000
## pctWInvInc                  0.51194 0.000000e+00 1.000000e+00   0.00000000
## pctWSocSec                  0.94747 1.000000e+00 1.000000e+00   1.00000000
## pctWPubAsst                 0.34965 1.000000e+00 1.000000e+00   0.00000000
## pctWRetire                  0.67101 1.000000e+00 1.000000e+00   1.00000000
## medFamInc                   0.37602 0.000000e+00 0.000000e+00   1.00000000
## whitePerCap                 0.81810 0.000000e+00 0.000000e+00   1.00000000
## blackPerCap                 0.40296 0.000000e+00 1.000000e+00   1.00000000
## indianPerCap                0.09702 0.000000e+00 0.000000e+00   0.00000000
## AsianPerCap                 0.25055 1.000000e+00 0.000000e+00   0.00000000
## OtherPerCap                 0.63448 0.000000e+00 1.000000e+00   1.00000000
## HispPerCap                  0.15612 0.000000e+00 0.000000e+00   0.00000000
## NumUnderPov                 0.15801 0.000000e+00 0.000000e+00   0.00000000
## PctPopUnderPov              0.99245 1.000000e+00 1.000000e+00   1.00000000
## PctLess9thGrade             0.91452 1.000000e+00 1.000000e+00   1.00000000
## PctBSorMore                 0.11348 0.000000e+00 0.000000e+00   0.00000000
## PctUnemployed               0.15265 0.000000e+00 0.000000e+00   0.00000000
## PctEmploy                   0.99129 1.000000e+00 1.000000e+00   1.00000000
## PctEmplManu                 0.52188 1.000000e+00 1.000000e+00   0.00000000
## PctEmplProfServ             0.68585 1.000000e+00 1.000000e+00   1.00000000
## PctOccupMgmtProf            0.57549 1.000000e+00 1.000000e+00   1.00000000
## MalePctNevMarr              0.74745 1.000000e+00 0.000000e+00   0.00000000
## TotalPctDiv                 0.99890 1.000000e+00 1.000000e+00   1.00000000
## PersPerFam                  0.18128 0.000000e+00 0.000000e+00   0.00000000
## PctFam2Par                  0.71090 1.000000e+00 1.000000e+00   1.00000000
## PctWorkMom                  0.11141 0.000000e+00 0.000000e+00   0.00000000
## PctKidsBornNeverMar         0.19325 0.000000e+00 1.000000e+00   0.00000000
## NumImmig                    0.14674 0.000000e+00 0.000000e+00   0.00000000
## PctImmigRecent              0.16265 0.000000e+00 0.000000e+00   0.00000000
## PctRecentImmig              0.92487 1.000000e+00 1.000000e+00   1.00000000
## PctSpeakEnglOnly            0.43800 1.000000e+00 0.000000e+00   1.00000000
## PctNotSpeakEnglWell         0.14099 0.000000e+00 0.000000e+00   0.00000000
## PctLargHouseFam             0.42139 0.000000e+00 0.000000e+00   1.00000000
## PersPerOccupHous            0.26344 0.000000e+00 0.000000e+00   0.00000000
## PersPerOwnOccHous           0.33684 0.000000e+00 0.000000e+00   1.00000000
## PersPerRentOccHous          0.50664 0.000000e+00 0.000000e+00   1.00000000
## PctPersOwnOccup             0.79563 0.000000e+00 1.000000e+00   1.00000000
## PctPersDenseHous            0.12412 0.000000e+00 0.000000e+00   0.00000000
## PctHousLess3BR              0.45678 1.000000e+00 1.000000e+00   1.00000000
## MedNumBR                    0.18598 1.000000e+00 0.000000e+00   0.00000000
## HousVacant                  0.22934 0.000000e+00 0.000000e+00   0.00000000
## PctHousOccup                0.24523 0.000000e+00 0.000000e+00   0.00000000
## PctHousOwnOcc               0.71144 1.000000e+00 1.000000e+00   0.00000000
## PctVacantBoarded            0.26650 0.000000e+00 1.000000e+00   0.00000000
## PctVacMore6Mos              0.45058 1.000000e+00 0.000000e+00   0.00000000
## MedYrHousBuilt              0.87986 1.000000e+00 1.000000e+00   1.00000000
## PctHousNoPhone              0.23198 1.000000e+00 0.000000e+00   0.00000000
## PctWOFullPlumb              0.09553 0.000000e+00 0.000000e+00   0.00000000
## OwnOccLowQuart              0.18770 0.000000e+00 0.000000e+00   0.00000000
## OwnOccMedVal                0.33140 1.000000e+00 0.000000e+00   0.00000000
## OwnOccHiQuart               0.28415 0.000000e+00 0.000000e+00   0.00000000
## RentLowQ                    0.27120 0.000000e+00 0.000000e+00   0.00000000
## RentMedian                  0.35819 0.000000e+00 0.000000e+00   1.00000000
## RentHighQ                   0.21633 1.000000e+00 0.000000e+00   0.00000000
## MedRent                     0.30726 0.000000e+00 1.000000e+00   1.00000000
## MedRentPctHousInc           0.24676 0.000000e+00 0.000000e+00   0.00000000
## MedOwnCostPctInc            0.91878 1.000000e+00 1.000000e+00   1.00000000
## MedOwnCostPctIncNoMtg       0.15125 0.000000e+00 0.000000e+00   0.00000000
## NumInShelters               0.82854 1.000000e+00 1.000000e+00   1.00000000
## NumStreet                   0.99240 1.000000e+00 1.000000e+00   1.00000000
## PctForeignBorn              0.88492 1.000000e+00 1.000000e+00   1.00000000
## PctBornSameState            0.53924 1.000000e+00 0.000000e+00   1.00000000
## PctSameHouse85              0.11558 0.000000e+00 0.000000e+00   0.00000000
## PctSameCity85               0.14933 0.000000e+00 0.000000e+00   0.00000000
## PctSameState85              0.21360 0.000000e+00 0.000000e+00   0.00000000
## LandArea                    0.86035 1.000000e+00 1.000000e+00   0.00000000
## PopDens                     0.99985 1.000000e+00 1.000000e+00   1.00000000
## PctUsePubTrans              0.10048 0.000000e+00 0.000000e+00   0.00000000
## LemasPctOfficDrugUn         0.43883 0.000000e+00 0.000000e+00   0.00000000
## agePct22t29                 0.15746 0.000000e+00 1.000000e+00   0.00000000
## BF                               NA 1.239982e-04 7.917376e-04   0.07980822
## PostProbs                        NA 4.000000e-04 3.000000e-04   0.00030000
## R2                               NA 4.672000e-01 4.669000e-01   0.46820000
## dim                              NA 3.400000e+01 3.300000e+01  32.00000000
## logmarg                          NA 5.046437e+02 5.064976e+02 511.11077649
##                            model 4  model 5
## Intercept             1.000000e+00   1.0000
## population            0.000000e+00   0.0000
## householdsize         0.000000e+00   0.0000
## racepctblack          0.000000e+00   1.0000
## racePctWhite          0.000000e+00   0.0000
## racePctAsian          0.000000e+00   0.0000
## racePctHisp           0.000000e+00   0.0000
## agePct12t29           0.000000e+00   1.0000
## agePct65up            1.000000e+00   0.0000
## numbUrban             0.000000e+00   0.0000
## pctUrban              0.000000e+00   0.0000
## medIncome             1.000000e+00   0.0000
## pctWWage              0.000000e+00   1.0000
## pctWFarmSelf          0.000000e+00   0.0000
## pctWInvInc            0.000000e+00   0.0000
## pctWSocSec            1.000000e+00   1.0000
## pctWPubAsst           0.000000e+00   0.0000
## pctWRetire            0.000000e+00   0.0000
## medFamInc             1.000000e+00   1.0000
## whitePerCap           1.000000e+00   1.0000
## blackPerCap           0.000000e+00   0.0000
## indianPerCap          0.000000e+00   0.0000
## AsianPerCap           0.000000e+00   0.0000
## OtherPerCap           1.000000e+00   1.0000
## HispPerCap            0.000000e+00   0.0000
## NumUnderPov           0.000000e+00   0.0000
## PctPopUnderPov        1.000000e+00   1.0000
## PctLess9thGrade       1.000000e+00   1.0000
## PctBSorMore           0.000000e+00   0.0000
## PctUnemployed         0.000000e+00   0.0000
## PctEmploy             1.000000e+00   1.0000
## PctEmplManu           0.000000e+00   0.0000
## PctEmplProfServ       0.000000e+00   1.0000
## PctOccupMgmtProf      0.000000e+00   1.0000
## MalePctNevMarr        1.000000e+00   1.0000
## TotalPctDiv           1.000000e+00   1.0000
## PersPerFam            0.000000e+00   0.0000
## PctFam2Par            1.000000e+00   1.0000
## PctWorkMom            0.000000e+00   0.0000
## PctKidsBornNeverMar   0.000000e+00   0.0000
## NumImmig              0.000000e+00   0.0000
## PctImmigRecent        0.000000e+00   1.0000
## PctRecentImmig        0.000000e+00   1.0000
## PctSpeakEnglOnly      1.000000e+00   0.0000
## PctNotSpeakEnglWell   0.000000e+00   0.0000
## PctLargHouseFam       0.000000e+00   0.0000
## PersPerOccupHous      0.000000e+00   0.0000
## PersPerOwnOccHous     1.000000e+00   1.0000
## PersPerRentOccHous    1.000000e+00   1.0000
## PctPersOwnOccup       1.000000e+00   1.0000
## PctPersDenseHous      1.000000e+00   0.0000
## PctHousLess3BR        0.000000e+00   0.0000
## MedNumBR              0.000000e+00   0.0000
## HousVacant            0.000000e+00   0.0000
## PctHousOccup          0.000000e+00   0.0000
## PctHousOwnOcc         1.000000e+00   1.0000
## PctVacantBoarded      1.000000e+00   0.0000
## PctVacMore6Mos        0.000000e+00   0.0000
## MedYrHousBuilt        1.000000e+00   1.0000
## PctHousNoPhone        1.000000e+00   0.0000
## PctWOFullPlumb        0.000000e+00   0.0000
## OwnOccLowQuart        0.000000e+00   0.0000
## OwnOccMedVal          1.000000e+00   0.0000
## OwnOccHiQuart         0.000000e+00   1.0000
## RentLowQ              0.000000e+00   0.0000
## RentMedian            0.000000e+00   1.0000
## RentHighQ             0.000000e+00   0.0000
## MedRent               0.000000e+00   0.0000
## MedRentPctHousInc     0.000000e+00   0.0000
## MedOwnCostPctInc      1.000000e+00   1.0000
## MedOwnCostPctIncNoMtg 0.000000e+00   0.0000
## NumInShelters         1.000000e+00   1.0000
## NumStreet             1.000000e+00   1.0000
## PctForeignBorn        0.000000e+00   1.0000
## PctBornSameState      1.000000e+00   1.0000
## PctSameHouse85        0.000000e+00   0.0000
## PctSameCity85         0.000000e+00   1.0000
## PctSameState85        0.000000e+00   0.0000
## LandArea              1.000000e+00   1.0000
## PopDens               1.000000e+00   1.0000
## PctUsePubTrans        0.000000e+00   0.0000
## LemasPctOfficDrugUn   1.000000e+00   0.0000
## agePct22t29           0.000000e+00   0.0000
## BF                    7.543113e-03   1.0000
## PostProbs             3.000000e-04   0.0003
## R2                    4.642000e-01   0.4710
## dim                   3.000000e+01  33.0000
## logmarg               5.087518e+02 513.6389

top 5 model

8.3 Visualization of the Model Space

image(fit.gprior, rotate=F)

8.4 Posterior Distributions of Coefficients

coef.gprior = coef(fit.gprior)
coef.gprior
## 
##  Marginal Posterior Summaries of Coefficients: 
## 
##  Using  BMA 
## 
##  Based on the top  27030 models 
##                        post mean   post SD     post p(B != 0)
## Intercept               3.370e+03   3.304e+01   1.000e+00    
## population             -1.642e+01   8.129e+01   1.855e-01    
## householdsize          -4.031e+01   1.061e+02   2.312e-01    
## racepctblack           -8.996e+00   4.811e+01   1.617e-01    
## racePctWhite            5.078e+00   3.959e+01   1.201e-01    
## racePctAsian            9.268e+00   3.182e+01   1.554e-01    
## racePctHisp            -1.130e+00   5.453e+01   1.486e-01    
## agePct12t29            -1.097e+02   1.753e+02   3.930e-01    
## agePct65up              1.127e+02   2.041e+02   3.246e-01    
## numbUrban              -1.524e+01   9.369e+01   1.188e-01    
## pctUrban                1.840e+01   9.212e+01   1.300e-01    
## medIncome              -6.458e+01   2.006e+02   2.317e-01    
## pctWWage                3.050e+02   2.550e+02   6.819e-01    
## pctWFarmSelf           -8.043e+00   2.550e+01   1.650e-01    
## pctWInvInc              1.277e+02   1.518e+02   5.119e-01    
## pctWSocSec              6.629e+02   2.504e+02   9.475e-01    
## pctWPubAsst            -6.484e+01   1.086e+02   3.497e-01    
## pctWRetire             -1.095e+02   9.526e+01   6.710e-01    
## medFamInc              -1.757e+02   2.771e+02   3.760e-01    
## whitePerCap             3.380e+02   2.222e+02   8.181e-01    
## blackPerCap            -3.085e+01   4.508e+01   4.030e-01    
## indianPerCap           -9.171e-01   1.062e+01   9.702e-02    
## AsianPerCap            -1.485e+01   3.253e+01   2.505e-01    
## OtherPerCap             5.394e+01   4.989e+01   6.345e-01    
## HispPerCap              8.777e+00   2.886e+01   1.561e-01    
## NumUnderPov             1.540e+01   9.406e+01   1.580e-01    
## PctPopUnderPov          6.345e+02   1.674e+02   9.925e-01    
## PctLess9thGrade        -2.558e+02   1.215e+02   9.145e-01    
## PctBSorMore            -8.392e+00   6.842e+01   1.135e-01    
## PctUnemployed          -1.382e+01   4.820e+01   1.527e-01    
## PctEmploy               4.887e+02   1.480e+02   9.913e-01    
## PctEmplManu            -6.231e+01   7.213e+01   5.219e-01    
## PctEmplProfServ        -1.430e+02   1.227e+02   6.858e-01    
## PctOccupMgmtProf        1.693e+02   1.784e+02   5.755e-01    
## MalePctNevMarr          2.551e+02   2.007e+02   7.474e-01    
## TotalPctDiv             4.949e+02   1.383e+02   9.989e-01    
## PersPerFam              7.683e+00   1.094e+02   1.813e-01    
## PctFam2Par             -3.215e+02   2.572e+02   7.109e-01    
## PctWorkMom             -2.906e+00   2.192e+01   1.114e-01    
## PctKidsBornNeverMar     2.333e+01   6.974e+01   1.933e-01    
## NumImmig                1.447e+01   6.176e+01   1.467e-01    
## PctImmigRecent          8.598e+00   2.875e+01   1.626e-01    
## PctRecentImmig         -3.280e+02   1.463e+02   9.249e-01    
## PctSpeakEnglOnly       -1.095e+02   1.550e+02   4.380e-01    
## PctNotSpeakEnglWell     1.632e+01   7.384e+01   1.410e-01    
## PctLargHouseFam         9.588e+01   1.424e+02   4.214e-01    
## PersPerOccupHous        9.228e+01   2.262e+02   2.634e-01    
## PersPerOwnOccHous       6.454e+01   2.337e+02   3.368e-01    
## PersPerRentOccHous     -1.884e+02   2.427e+02   5.066e-01    
## PctPersOwnOccup        -1.261e+03   1.134e+03   7.956e-01    
## PctPersDenseHous       -3.917e+00   5.156e+01   1.241e-01    
## PctHousLess3BR         -9.615e+01   1.282e+02   4.568e-01    
## MedNumBR               -1.346e+01   3.809e+01   1.860e-01    
## HousVacant             -1.571e+01   3.724e+01   2.293e-01    
## PctHousOccup           -1.866e+01   4.111e+01   2.452e-01    
## PctHousOwnOcc           1.025e+03   1.057e+03   7.114e-01    
## PctVacantBoarded       -2.089e+01   4.342e+01   2.665e-01    
## PctVacMore6Mos         -4.555e+01   6.091e+01   4.506e-01    
## MedYrHousBuilt          1.869e+02   9.809e+01   8.799e-01    
## PctHousNoPhone          2.976e+01   6.994e+01   2.320e-01    
## PctWOFullPlumb         -1.057e+00   1.430e+01   9.553e-02    
## OwnOccLowQuart         -2.921e+01   1.021e+02   1.877e-01    
## OwnOccMedVal           -8.534e+01   1.549e+02   3.314e-01    
## OwnOccHiQuart          -6.438e+01   1.294e+02   2.842e-01    
## RentLowQ               -5.426e+01   1.109e+02   2.712e-01    
## RentMedian             -1.106e+02   1.863e+02   3.582e-01    
## RentHighQ              -5.105e+01   1.311e+02   2.163e-01    
## MedRent                -8.076e+01   1.586e+02   3.073e-01    
## MedRentPctHousInc      -2.225e+01   4.931e+01   2.468e-01    
## MedOwnCostPctInc       -1.858e+02   8.388e+01   9.188e-01    
## MedOwnCostPctIncNoMtg   7.900e+00   2.681e+01   1.512e-01    
## NumInShelters           1.219e+02   7.326e+01   8.285e-01    
## NumStreet               1.879e+02   5.306e+01   9.924e-01    
## PctForeignBorn          4.553e+02   2.293e+02   8.849e-01    
## PctBornSameState       -7.269e+01   8.160e+01   5.392e-01    
## PctSameHouse85          4.929e+00   3.984e+01   1.156e-01    
## PctSameCity85           7.959e+00   3.712e+01   1.493e-01    
## PctSameState85         -1.704e+01   4.840e+01   2.136e-01    
## LandArea               -1.604e+02   8.953e+01   8.603e-01    
## PopDens                -3.907e+02   7.301e+01   9.999e-01    
## PctUsePubTrans          3.712e-01   1.832e+01   1.005e-01    
## LemasPctOfficDrugUn     3.531e+01   4.777e+01   4.388e-01    
## agePct22t29            -1.557e+01   5.172e+01   1.575e-01

8.4.1 individual plot

probne0 > 0.2

survivors = which(coef.gprior$probne0 > 0.2)
plot(coef.gprior, subset = survivors, ask = F)

8.4.2 coefficient plot

plot(confint(coef.gprior, parm = survivors))

## NULL

8.5 Prediction

muhat.bma <- fitted(fit.gprior, estimator = "BMA")
bma <- predict(fit.gprior, estimator = "BMA", newdata = data)

result_data = original_data %>%
  mutate(pred_y=bma$fit)
## Warning: Ignoring 3 observations

9 autoTheftPerPop

y_name = 'autoTheftPerPop'

9.1 Model fit

f = paste(y_name, " ~ . -murdPerPop -rapesPerPop -robbbPerPop -assaultPerPop -burglPerPop -larcPerPop -autoTheftPerPop -arsonsPerPop")

fit.gprior = bas.lm(f,
                    data = data,
                    method = "MCMC", # better than default "BAS"
                                     # for large p
                   prior = "ZS-null", # default
                                      # "JZS" also can use
                   modelprior = uniform(),
                   include.always = ~1,
                   MCMC.iterations = 100000)
## Warning in bas.lm(f, data = data, method = "MCMC", prior = "ZS-null", modelprior
## = uniform(), : dropping 313 rows due to missing data
plot(fit.gprior, ask = F)

9.2 model result

summary(fit.gprior)
##                       P(B != 0 | Y)      model 1      model 2  model 3
## Intercept                   1.00000 1.000000e+00 1.000000e+00   1.0000
## population                  0.45658 0.000000e+00 0.000000e+00   0.0000
## householdsize               0.54852 0.000000e+00 0.000000e+00   0.0000
## racepctblack                0.17508 0.000000e+00 0.000000e+00   0.0000
## racePctWhite                0.92562 1.000000e+00 1.000000e+00   1.0000
## racePctAsian                0.94482 1.000000e+00 1.000000e+00   1.0000
## racePctHisp                 0.19471 0.000000e+00 0.000000e+00   1.0000
## agePct12t29                 0.26319 0.000000e+00 1.000000e+00   0.0000
## agePct65up                  0.13078 0.000000e+00 0.000000e+00   0.0000
## numbUrban                   0.25717 0.000000e+00 0.000000e+00   0.0000
## pctUrban                    0.27850 1.000000e+00 0.000000e+00   0.0000
## medIncome                   0.67072 1.000000e+00 0.000000e+00   1.0000
## pctWWage                    0.09838 0.000000e+00 0.000000e+00   0.0000
## pctWFarmSelf                0.49571 0.000000e+00 0.000000e+00   0.0000
## pctWInvInc                  0.96817 1.000000e+00 1.000000e+00   1.0000
## pctWSocSec                  0.99041 1.000000e+00 1.000000e+00   1.0000
## pctWPubAsst                 0.13800 1.000000e+00 0.000000e+00   0.0000
## pctWRetire                  0.71547 1.000000e+00 1.000000e+00   0.0000
## medFamInc                   0.25732 0.000000e+00 1.000000e+00   0.0000
## whitePerCap                 0.13733 0.000000e+00 0.000000e+00   0.0000
## blackPerCap                 0.11752 0.000000e+00 0.000000e+00   0.0000
## indianPerCap                0.08756 0.000000e+00 0.000000e+00   0.0000
## AsianPerCap                 0.07559 0.000000e+00 0.000000e+00   0.0000
## OtherPerCap                 0.08115 0.000000e+00 0.000000e+00   0.0000
## HispPerCap                  0.12514 0.000000e+00 0.000000e+00   0.0000
## NumUnderPov                 0.26766 0.000000e+00 1.000000e+00   0.0000
## PctPopUnderPov              0.49839 0.000000e+00 0.000000e+00   0.0000
## PctLess9thGrade             0.90519 1.000000e+00 1.000000e+00   1.0000
## PctBSorMore                 0.27801 0.000000e+00 1.000000e+00   0.0000
## PctUnemployed               0.11700 0.000000e+00 0.000000e+00   0.0000
## PctEmploy                   0.67665 1.000000e+00 1.000000e+00   1.0000
## PctEmplManu                 0.09823 0.000000e+00 0.000000e+00   0.0000
## PctEmplProfServ             0.09062 0.000000e+00 0.000000e+00   0.0000
## PctOccupMgmtProf            0.28397 0.000000e+00 1.000000e+00   0.0000
## MalePctNevMarr              0.99884 1.000000e+00 1.000000e+00   1.0000
## TotalPctDiv                 0.99939 1.000000e+00 1.000000e+00   1.0000
## PersPerFam                  0.26381 0.000000e+00 1.000000e+00   0.0000
## PctFam2Par                  0.16131 0.000000e+00 0.000000e+00   0.0000
## PctWorkMom                  0.99920 1.000000e+00 1.000000e+00   1.0000
## PctKidsBornNeverMar         0.12426 0.000000e+00 0.000000e+00   0.0000
## NumImmig                    0.44576 1.000000e+00 0.000000e+00   1.0000
## PctImmigRecent              0.11447 0.000000e+00 0.000000e+00   0.0000
## PctRecentImmig              0.93874 1.000000e+00 1.000000e+00   1.0000
## PctSpeakEnglOnly            0.13118 1.000000e+00 0.000000e+00   0.0000
## PctNotSpeakEnglWell         0.23462 0.000000e+00 0.000000e+00   0.0000
## PctLargHouseFam             0.84617 1.000000e+00 0.000000e+00   1.0000
## PersPerOccupHous            0.62624 1.000000e+00 1.000000e+00   1.0000
## PersPerOwnOccHous           0.99860 1.000000e+00 1.000000e+00   1.0000
## PersPerRentOccHous          0.80548 1.000000e+00 1.000000e+00   1.0000
## PctPersOwnOccup             0.99821 1.000000e+00 1.000000e+00   1.0000
## PctPersDenseHous            0.28365 0.000000e+00 0.000000e+00   1.0000
## PctHousLess3BR              0.91887 1.000000e+00 1.000000e+00   1.0000
## MedNumBR                    0.12216 1.000000e+00 0.000000e+00   0.0000
## HousVacant                  0.08147 0.000000e+00 0.000000e+00   0.0000
## PctHousOccup                0.30329 0.000000e+00 0.000000e+00   0.0000
## PctHousOwnOcc               0.99871 1.000000e+00 1.000000e+00   1.0000
## PctVacantBoarded            0.94362 1.000000e+00 1.000000e+00   1.0000
## PctVacMore6Mos              0.97472 1.000000e+00 1.000000e+00   1.0000
## MedYrHousBuilt              0.09221 0.000000e+00 0.000000e+00   0.0000
## PctHousNoPhone              0.85286 1.000000e+00 1.000000e+00   1.0000
## PctWOFullPlumb              0.08341 0.000000e+00 0.000000e+00   0.0000
## OwnOccLowQuart              0.76448 1.000000e+00 1.000000e+00   1.0000
## OwnOccMedVal                0.27768 1.000000e+00 0.000000e+00   0.0000
## OwnOccHiQuart               0.40580 1.000000e+00 1.000000e+00   0.0000
## RentLowQ                    0.11556 0.000000e+00 0.000000e+00   0.0000
## RentMedian                  0.11174 0.000000e+00 0.000000e+00   0.0000
## RentHighQ                   0.24823 0.000000e+00 1.000000e+00   0.0000
## MedRent                     0.10197 0.000000e+00 0.000000e+00   0.0000
## MedRentPctHousInc           0.16399 0.000000e+00 0.000000e+00   0.0000
## MedOwnCostPctInc            0.12654 0.000000e+00 0.000000e+00   0.0000
## MedOwnCostPctIncNoMtg       0.95371 1.000000e+00 1.000000e+00   1.0000
## NumInShelters               0.30263 0.000000e+00 1.000000e+00   0.0000
## NumStreet                   0.99788 1.000000e+00 1.000000e+00   1.0000
## PctForeignBorn              0.99942 1.000000e+00 1.000000e+00   1.0000
## PctBornSameState            0.10312 0.000000e+00 0.000000e+00   0.0000
## PctSameHouse85              0.22440 1.000000e+00 0.000000e+00   0.0000
## PctSameCity85               0.64611 0.000000e+00 1.000000e+00   1.0000
## PctSameState85              0.11745 0.000000e+00 0.000000e+00   0.0000
## LandArea                    0.11988 0.000000e+00 0.000000e+00   0.0000
## PopDens                     0.29345 0.000000e+00 0.000000e+00   0.0000
## PctUsePubTrans              0.82459 0.000000e+00 0.000000e+00   1.0000
## LemasPctOfficDrugUn         0.21160 0.000000e+00 0.000000e+00   0.0000
## agePct22t29                 0.13027 0.000000e+00 0.000000e+00   1.0000
## BF                               NA 4.890769e-04 5.454184e-03   1.0000
## PostProbs                        NA 6.000000e-04 6.000000e-04   0.0006
## R2                               NA 5.914000e-01 5.925000e-01   0.5915
## dim                              NA 3.500000e+01 3.500000e+01  32.0000
## logmarg                          NA 7.499679e+02 7.523795e+02 757.5909
##                            model 4      model 5
## Intercept             1.000000e+00 1.000000e+00
## population            0.000000e+00 0.000000e+00
## householdsize         0.000000e+00 0.000000e+00
## racepctblack          1.000000e+00 0.000000e+00
## racePctWhite          1.000000e+00 1.000000e+00
## racePctAsian          1.000000e+00 1.000000e+00
## racePctHisp           0.000000e+00 1.000000e+00
## agePct12t29           0.000000e+00 0.000000e+00
## agePct65up            0.000000e+00 0.000000e+00
## numbUrban             0.000000e+00 0.000000e+00
## pctUrban              1.000000e+00 0.000000e+00
## medIncome             1.000000e+00 0.000000e+00
## pctWWage              0.000000e+00 0.000000e+00
## pctWFarmSelf          0.000000e+00 0.000000e+00
## pctWInvInc            1.000000e+00 1.000000e+00
## pctWSocSec            1.000000e+00 1.000000e+00
## pctWPubAsst           0.000000e+00 0.000000e+00
## pctWRetire            1.000000e+00 1.000000e+00
## medFamInc             0.000000e+00 1.000000e+00
## whitePerCap           0.000000e+00 0.000000e+00
## blackPerCap           0.000000e+00 0.000000e+00
## indianPerCap          0.000000e+00 0.000000e+00
## AsianPerCap           0.000000e+00 0.000000e+00
## OtherPerCap           0.000000e+00 0.000000e+00
## HispPerCap            0.000000e+00 0.000000e+00
## NumUnderPov           1.000000e+00 0.000000e+00
## PctPopUnderPov        0.000000e+00 0.000000e+00
## PctLess9thGrade       1.000000e+00 0.000000e+00
## PctBSorMore           1.000000e+00 0.000000e+00
## PctUnemployed         0.000000e+00 0.000000e+00
## PctEmploy             1.000000e+00 1.000000e+00
## PctEmplManu           0.000000e+00 0.000000e+00
## PctEmplProfServ       0.000000e+00 0.000000e+00
## PctOccupMgmtProf      0.000000e+00 0.000000e+00
## MalePctNevMarr        1.000000e+00 1.000000e+00
## TotalPctDiv           1.000000e+00 1.000000e+00
## PersPerFam            0.000000e+00 0.000000e+00
## PctFam2Par            0.000000e+00 1.000000e+00
## PctWorkMom            1.000000e+00 1.000000e+00
## PctKidsBornNeverMar   0.000000e+00 0.000000e+00
## NumImmig              1.000000e+00 1.000000e+00
## PctImmigRecent        0.000000e+00 0.000000e+00
## PctRecentImmig        1.000000e+00 1.000000e+00
## PctSpeakEnglOnly      0.000000e+00 0.000000e+00
## PctNotSpeakEnglWell   0.000000e+00 0.000000e+00
## PctLargHouseFam       1.000000e+00 1.000000e+00
## PersPerOccupHous      1.000000e+00 1.000000e+00
## PersPerOwnOccHous     1.000000e+00 1.000000e+00
## PersPerRentOccHous    1.000000e+00 1.000000e+00
## PctPersOwnOccup       1.000000e+00 1.000000e+00
## PctPersDenseHous      0.000000e+00 0.000000e+00
## PctHousLess3BR        1.000000e+00 1.000000e+00
## MedNumBR              0.000000e+00 0.000000e+00
## HousVacant            0.000000e+00 1.000000e+00
## PctHousOccup          0.000000e+00 1.000000e+00
## PctHousOwnOcc         1.000000e+00 1.000000e+00
## PctVacantBoarded      1.000000e+00 1.000000e+00
## PctVacMore6Mos        1.000000e+00 1.000000e+00
## MedYrHousBuilt        0.000000e+00 0.000000e+00
## PctHousNoPhone        1.000000e+00 1.000000e+00
## PctWOFullPlumb        0.000000e+00 0.000000e+00
## OwnOccLowQuart        1.000000e+00 1.000000e+00
## OwnOccMedVal          0.000000e+00 0.000000e+00
## OwnOccHiQuart         0.000000e+00 0.000000e+00
## RentLowQ              0.000000e+00 0.000000e+00
## RentMedian            0.000000e+00 0.000000e+00
## RentHighQ             1.000000e+00 0.000000e+00
## MedRent               0.000000e+00 0.000000e+00
## MedRentPctHousInc     0.000000e+00 0.000000e+00
## MedOwnCostPctInc      0.000000e+00 0.000000e+00
## MedOwnCostPctIncNoMtg 1.000000e+00 1.000000e+00
## NumInShelters         1.000000e+00 1.000000e+00
## NumStreet             1.000000e+00 1.000000e+00
## PctForeignBorn        1.000000e+00 1.000000e+00
## PctBornSameState      0.000000e+00 0.000000e+00
## PctSameHouse85        0.000000e+00 0.000000e+00
## PctSameCity85         1.000000e+00 1.000000e+00
## PctSameState85        0.000000e+00 0.000000e+00
## LandArea              0.000000e+00 0.000000e+00
## PopDens               0.000000e+00 0.000000e+00
## PctUsePubTrans        1.000000e+00 1.000000e+00
## LemasPctOfficDrugUn   0.000000e+00 0.000000e+00
## agePct22t29           0.000000e+00 0.000000e+00
## BF                    5.690978e-03 2.486134e-03
## PostProbs             6.000000e-04 5.000000e-04
## R2                    5.936000e-01 5.910000e-01
## dim                   3.600000e+01 3.400000e+01
## logmarg               7.524220e+02 7.515938e+02

top 5 model

9.3 Visualization of the Model Space

image(fit.gprior, rotate=F)

9.4 Posterior Distributions of Coefficients

coef.gprior = coef(fit.gprior)
coef.gprior
## 
##  Marginal Posterior Summaries of Coefficients: 
## 
##  Using  BMA 
## 
##  Based on the top  19810 models 
##                        post mean   post SD     post p(B != 0)
## Intercept               483.27783     7.49098     1.00000    
## population               20.45982    27.16575     0.45658    
## householdsize           -47.27980    50.93074     0.54852    
## racepctblack             10.17035    30.30249     0.17508    
## racePctWhite           -120.37727    41.06337     0.92562    
## racePctAsian            -50.95543    18.52333     0.94482    
## racePctHisp              -6.14658    17.16623     0.19471    
## agePct12t29             -14.18694    29.26382     0.26319    
## agePct65up                4.80909    21.70564     0.13078    
## numbUrban                 5.44792    13.17481     0.25717    
## pctUrban                  5.72908    12.68340     0.27850    
## medIncome                84.31681    71.25286     0.67072    
## pctWWage                 -1.79944    13.74895     0.09838    
## pctWFarmSelf             10.50581    12.57979     0.49571    
## pctWInvInc              -95.88972    34.41879     0.96817    
## pctWSocSec              148.91534    36.81554     0.99041    
## pctWPubAsst               3.12970    11.53596     0.13800    
## pctWRetire              -29.66026    23.44896     0.71547    
## medFamInc                19.97747    50.00781     0.25732    
## whitePerCap               3.75081    16.45259     0.13733    
## blackPerCap              -0.73142     3.68434     0.11752    
## indianPerCap             -0.27464     2.38245     0.08756    
## AsianPerCap              -0.08687     2.50665     0.07559    
## OtherPerCap               0.27128     2.47941     0.08115    
## HispPerCap                0.90848     4.50890     0.12514    
## NumUnderPov              12.25371    28.83041     0.26766    
## PctPopUnderPov          -45.10923    54.63946     0.49839    
## PctLess9thGrade         -62.06848    28.87602     0.90519    
## PctBSorMore             -19.42713    40.29858     0.27801    
## PctUnemployed             1.85347     8.87726     0.11700    
## PctEmploy                60.35750    49.50913     0.67665    
## PctEmplManu               0.38817     3.75740     0.09823    
## PctEmplProfServ          -0.32204     4.82373     0.09062    
## PctOccupMgmtProf         16.64815    34.13959     0.28397    
## MalePctNevMarr          163.33069    32.39099     0.99884    
## TotalPctDiv             129.39465    25.66146     0.99939    
## PersPerFam              -27.87587    57.71270     0.26381    
## PctFam2Par                7.44426    23.84257     0.16131    
## PctWorkMom              -63.95244    14.06450     0.99920    
## PctKidsBornNeverMar       2.76186    12.26678     0.12426    
## NumImmig                 26.74120    34.95048     0.44576    
## PctImmigRecent           -0.46291     4.34993     0.11447    
## PctRecentImmig          -71.89477    29.31873     0.93874    
## PctSpeakEnglOnly         -0.59736    15.09367     0.13118    
## PctNotSpeakEnglWell     -13.12669    30.05745     0.23462    
## PctLargHouseFam         -84.33084    47.03689     0.84617    
## PersPerOccupHous       -163.82161   152.09552     0.62624    
## PersPerOwnOccHous       368.38379    93.16978     0.99860    
## PersPerRentOccHous      -85.18688    54.22476     0.80548    
## PctPersOwnOccup        -900.85344   262.28496     0.99821    
## PctPersDenseHous         18.55940    37.23479     0.28365    
## PctHousLess3BR           69.22595    30.42090     0.91887    
## MedNumBR                 -1.01933     5.44166     0.12216    
## HousVacant                0.17626     3.28382     0.08147    
## PctHousOccup             -5.46652    10.19620     0.30329    
## PctHousOwnOcc           926.87289   257.12278     0.99871    
## PctVacantBoarded         35.41376    13.98042     0.94362    
## PctVacMore6Mos          -38.42935    12.91190     0.97472    
## MedYrHousBuilt            0.62707     5.37681     0.09221    
## PctHousNoPhone          -52.11285    28.96249     0.85286    
## PctWOFullPlumb           -0.31396     3.10348     0.08341    
## OwnOccLowQuart         -100.38977    77.15622     0.76448    
## OwnOccMedVal             15.02399    93.68534     0.27768    
## OwnOccHiQuart           -39.53362    59.38814     0.40580    
## RentLowQ                 -1.53653    10.23434     0.11556    
## RentMedian               -0.35983    15.99421     0.11174    
## RentHighQ               -12.54486    28.70553     0.24823    
## MedRent                   0.88864    15.62696     0.10197    
## MedRentPctHousInc        -2.37696     7.65239     0.16399    
## MedOwnCostPctInc         -1.61377     7.33557     0.12654    
## MedOwnCostPctIncNoMtg   -33.13786    12.96531     0.95371    
## NumInShelters            -6.60329    11.99820     0.30263    
## NumStreet                65.41308    11.43249     0.99788    
## PctForeignBorn          237.73700    42.49077     0.99942    
## PctBornSameState         -0.34411     5.33192     0.10312    
## PctSameHouse85            7.16135    17.63864     0.22440    
## PctSameCity85            26.33473    23.51942     0.64611    
## PctSameState85            0.80950     5.98529     0.11745    
## LandArea                  0.29037     6.35890     0.11988    
## PopDens                  -7.39092    14.09756     0.29345    
## PctUsePubTrans           27.97856    17.36209     0.82459    
## LemasPctOfficDrugUn       2.91398     6.97319     0.21160    
## agePct22t29              -2.31836     9.01129     0.13027

9.4.1 individual plot

probne0 > 0.2

survivors = which(coef.gprior$probne0 > 0.2)
plot(coef.gprior, subset = survivors, ask = F)

9.4.2 coefficient plot

plot(confint(coef.gprior, parm = survivors))

## NULL

9.5 Prediction

muhat.bma <- fitted(fit.gprior, estimator = "BMA")
bma <- predict(fit.gprior, estimator = "BMA", newdata = data)

result_data = original_data %>%
  mutate(pred_y=bma$fit)
## Warning: Ignoring 3 observations

10 arsonsPerPop

y_name = 'arsonsPerPop'

10.1 Model fit

f = paste(y_name, " ~ . -murdPerPop -rapesPerPop -robbbPerPop -assaultPerPop -burglPerPop -larcPerPop -autoTheftPerPop -arsonsPerPop")

fit.gprior = bas.lm(f,
                    data = data,
                    method = "MCMC", # better than default "BAS"
                                     # for large p
                   prior = "ZS-null", # default
                                      # "JZS" also can use
                   modelprior = uniform(),
                   include.always = ~1,
                   MCMC.iterations = 100000)
## Warning in bas.lm(f, data = data, method = "MCMC", prior = "ZS-null", modelprior
## = uniform(), : dropping 313 rows due to missing data
plot(fit.gprior, ask = F)

10.2 model result

summary(fit.gprior)
##                       P(B != 0 | Y)      model 1     model 2    model 3
## Intercept                   1.00000   1.00000000   1.0000000   1.000000
## population                  0.40424   1.00000000   0.0000000   0.000000
## householdsize               0.11063   0.00000000   0.0000000   1.000000
## racepctblack                0.30800   0.00000000   1.0000000   0.000000
## racePctWhite                0.38524   0.00000000   1.0000000   0.000000
## racePctAsian                0.16385   0.00000000   0.0000000   0.000000
## racePctHisp                 0.19265   0.00000000   0.0000000   0.000000
## agePct12t29                 0.14444   0.00000000   0.0000000   0.000000
## agePct65up                  0.12009   0.00000000   0.0000000   0.000000
## numbUrban                   0.48569   1.00000000   1.0000000   1.000000
## pctUrban                    0.45996   0.00000000   0.0000000   0.000000
## medIncome                   0.12839   0.00000000   0.0000000   0.000000
## pctWWage                    0.21667   0.00000000   0.0000000   0.000000
## pctWFarmSelf                0.09340   1.00000000   0.0000000   0.000000
## pctWInvInc                  0.29442   0.00000000   0.0000000   0.000000
## pctWSocSec                  0.13551   0.00000000   0.0000000   0.000000
## pctWPubAsst                 0.96497   1.00000000   1.0000000   1.000000
## pctWRetire                  0.08704   1.00000000   0.0000000   0.000000
## medFamInc                   0.14752   0.00000000   0.0000000   0.000000
## whitePerCap                 0.31434   0.00000000   0.0000000   0.000000
## blackPerCap                 0.10668   0.00000000   0.0000000   0.000000
## indianPerCap                0.07877   0.00000000   0.0000000   0.000000
## AsianPerCap                 0.17188   0.00000000   0.0000000   0.000000
## OtherPerCap                 0.33760   0.00000000   0.0000000   0.000000
## HispPerCap                  0.08407   0.00000000   0.0000000   0.000000
## NumUnderPov                 0.14618   0.00000000   0.0000000   0.000000
## PctPopUnderPov              0.35704   0.00000000   1.0000000   0.000000
## PctLess9thGrade             0.69271   1.00000000   0.0000000   0.000000
## PctBSorMore                 0.12990   0.00000000   0.0000000   0.000000
## PctUnemployed               0.11484   0.00000000   0.0000000   0.000000
## PctEmploy                   0.12119   0.00000000   0.0000000   0.000000
## PctEmplManu                 0.45668   1.00000000   0.0000000   0.000000
## PctEmplProfServ             0.09596   0.00000000   0.0000000   0.000000
## PctOccupMgmtProf            0.15517   0.00000000   0.0000000   0.000000
## MalePctNevMarr              0.19976   0.00000000   0.0000000   0.000000
## TotalPctDiv                 0.99203   1.00000000   1.0000000   1.000000
## PersPerFam                  0.11076   0.00000000   0.0000000   0.000000
## PctFam2Par                  0.16089   0.00000000   0.0000000   1.000000
## PctWorkMom                  0.12742   0.00000000   0.0000000   0.000000
## PctKidsBornNeverMar         0.13533   0.00000000   0.0000000   0.000000
## NumImmig                    0.68463   0.00000000   1.0000000   1.000000
## PctImmigRecent              0.08400   0.00000000   0.0000000   0.000000
## PctRecentImmig              0.11577   0.00000000   0.0000000   0.000000
## PctSpeakEnglOnly            0.13692   0.00000000   1.0000000   0.000000
## PctNotSpeakEnglWell         0.16348   0.00000000   0.0000000   0.000000
## PctLargHouseFam             0.11041   1.00000000   0.0000000   0.000000
## PersPerOccupHous            0.15867   0.00000000   0.0000000   0.000000
## PersPerOwnOccHous           0.11844   0.00000000   1.0000000   0.000000
## PersPerRentOccHous          0.15993   0.00000000   1.0000000   0.000000
## PctPersOwnOccup             0.10484   0.00000000   0.0000000   0.000000
## PctPersDenseHous            0.14153   0.00000000   0.0000000   0.000000
## PctHousLess3BR              0.18842   0.00000000   0.0000000   0.000000
## MedNumBR                    0.20651   0.00000000   0.0000000   0.000000
## HousVacant                  0.10180   0.00000000   0.0000000   0.000000
## PctHousOccup                0.09873   0.00000000   0.0000000   0.000000
## PctHousOwnOcc               0.09108   0.00000000   0.0000000   0.000000
## PctVacantBoarded            0.99926   1.00000000   1.0000000   1.000000
## PctVacMore6Mos              0.11226   0.00000000   0.0000000   0.000000
## MedYrHousBuilt              0.10893   0.00000000   0.0000000   0.000000
## PctHousNoPhone              0.22986   1.00000000   0.0000000   0.000000
## PctWOFullPlumb              0.23707   0.00000000   0.0000000   1.000000
## OwnOccLowQuart              0.12030   0.00000000   0.0000000   0.000000
## OwnOccMedVal                0.20460   0.00000000   0.0000000   0.000000
## OwnOccHiQuart               0.15785   0.00000000   0.0000000   0.000000
## RentLowQ                    0.20174   0.00000000   0.0000000   1.000000
## RentMedian                  0.10260   0.00000000   0.0000000   0.000000
## RentHighQ                   0.12826   1.00000000   0.0000000   0.000000
## MedRent                     0.11401   0.00000000   0.0000000   0.000000
## MedRentPctHousInc           0.46039   0.00000000   0.0000000   1.000000
## MedOwnCostPctInc            0.13339   0.00000000   0.0000000   0.000000
## MedOwnCostPctIncNoMtg       0.13480   0.00000000   0.0000000   0.000000
## NumInShelters               0.95746   1.00000000   1.0000000   1.000000
## NumStreet                   0.08855   0.00000000   0.0000000   0.000000
## PctForeignBorn              0.50137   0.00000000   0.0000000   1.000000
## PctBornSameState            0.24769   1.00000000   0.0000000   1.000000
## PctSameHouse85              0.13375   0.00000000   0.0000000   0.000000
## PctSameCity85               0.12579   0.00000000   0.0000000   0.000000
## PctSameState85              0.22548   0.00000000   0.0000000   1.000000
## LandArea                    0.17502   0.00000000   0.0000000   0.000000
## PopDens                     0.12907   1.00000000   0.0000000   0.000000
## PctUsePubTrans              0.13151   0.00000000   0.0000000   0.000000
## LemasPctOfficDrugUn         0.08584   0.00000000   0.0000000   0.000000
## agePct22t29                 0.24852   0.00000000   0.0000000   0.000000
## BF                               NA   0.00119545   0.5664238   0.067863
## PostProbs                        NA   0.00040000   0.0003000   0.000300
## R2                               NA   0.27700000   0.2757000   0.278100
## dim                              NA  16.00000000  13.0000000  15.000000
## logmarg                          NA 262.09284398 268.2536638 266.131812
##                            model 4  model 5
## Intercept               1.00000000   1.0000
## population              1.00000000   0.0000
## householdsize           0.00000000   0.0000
## racepctblack            0.00000000   1.0000
## racePctWhite            0.00000000   1.0000
## racePctAsian            1.00000000   0.0000
## racePctHisp             0.00000000   0.0000
## agePct12t29             0.00000000   0.0000
## agePct65up              0.00000000   1.0000
## numbUrban               1.00000000   0.0000
## pctUrban                0.00000000   1.0000
## medIncome               0.00000000   0.0000
## pctWWage                0.00000000   1.0000
## pctWFarmSelf            0.00000000   0.0000
## pctWInvInc              1.00000000   0.0000
## pctWSocSec              0.00000000   0.0000
## pctWPubAsst             1.00000000   1.0000
## pctWRetire              0.00000000   0.0000
## medFamInc               0.00000000   0.0000
## whitePerCap             0.00000000   0.0000
## blackPerCap             0.00000000   0.0000
## indianPerCap            0.00000000   0.0000
## AsianPerCap             0.00000000   0.0000
## OtherPerCap             0.00000000   0.0000
## HispPerCap              0.00000000   0.0000
## NumUnderPov             0.00000000   0.0000
## PctPopUnderPov          0.00000000   0.0000
## PctLess9thGrade         1.00000000   1.0000
## PctBSorMore             0.00000000   0.0000
## PctUnemployed           1.00000000   0.0000
## PctEmploy               0.00000000   0.0000
## PctEmplManu             0.00000000   1.0000
## PctEmplProfServ         0.00000000   0.0000
## PctOccupMgmtProf        1.00000000   0.0000
## MalePctNevMarr          0.00000000   0.0000
## TotalPctDiv             1.00000000   1.0000
## PersPerFam              0.00000000   0.0000
## PctFam2Par              0.00000000   0.0000
## PctWorkMom              0.00000000   0.0000
## PctKidsBornNeverMar     0.00000000   0.0000
## NumImmig                0.00000000   1.0000
## PctImmigRecent          0.00000000   0.0000
## PctRecentImmig          0.00000000   0.0000
## PctSpeakEnglOnly        0.00000000   0.0000
## PctNotSpeakEnglWell     0.00000000   0.0000
## PctLargHouseFam         1.00000000   0.0000
## PersPerOccupHous        0.00000000   0.0000
## PersPerOwnOccHous       0.00000000   0.0000
## PersPerRentOccHous      0.00000000   0.0000
## PctPersOwnOccup         0.00000000   0.0000
## PctPersDenseHous        0.00000000   0.0000
## PctHousLess3BR          0.00000000   0.0000
## MedNumBR                0.00000000   0.0000
## HousVacant              0.00000000   0.0000
## PctHousOccup            0.00000000   0.0000
## PctHousOwnOcc           0.00000000   0.0000
## PctVacantBoarded        1.00000000   1.0000
## PctVacMore6Mos          0.00000000   0.0000
## MedYrHousBuilt          1.00000000   0.0000
## PctHousNoPhone          0.00000000   0.0000
## PctWOFullPlumb          0.00000000   0.0000
## OwnOccLowQuart          0.00000000   0.0000
## OwnOccMedVal            0.00000000   0.0000
## OwnOccHiQuart           0.00000000   0.0000
## RentLowQ                0.00000000   1.0000
## RentMedian              1.00000000   0.0000
## RentHighQ               0.00000000   0.0000
## MedRent                 0.00000000   0.0000
## MedRentPctHousInc       0.00000000   1.0000
## MedOwnCostPctInc        0.00000000   0.0000
## MedOwnCostPctIncNoMtg   0.00000000   1.0000
## NumInShelters           1.00000000   1.0000
## NumStreet               0.00000000   0.0000
## PctForeignBorn          0.00000000   1.0000
## PctBornSameState        0.00000000   0.0000
## PctSameHouse85          0.00000000   0.0000
## PctSameCity85           0.00000000   0.0000
## PctSameState85          0.00000000   0.0000
## LandArea                0.00000000   0.0000
## PopDens                 0.00000000   0.0000
## PctUsePubTrans          0.00000000   0.0000
## LemasPctOfficDrugUn     0.00000000   0.0000
## agePct22t29             0.00000000   0.0000
## BF                      0.03599546   1.0000
## PostProbs               0.00030000   0.0003
## R2                      0.27760000   0.2841
## dim                    15.00000000  17.0000
## logmarg               265.49771396 268.8221

top 5 model

10.3 Visualization of the Model Space

image(fit.gprior, rotate=F)

10.4 Posterior Distributions of Coefficients

coef.gprior = coef(fit.gprior)
coef.gprior
## 
##  Marginal Posterior Summaries of Coefficients: 
## 
##  Using  BMA 
## 
##  Based on the top  31641 models 
##                        post mean  post SD    post p(B != 0)
## Intercept              32.040573   0.773408   1.000000     
## population              2.143175   3.186054   0.404240     
## householdsize           0.076734   0.712860   0.110630     
## racepctblack           -1.573752   3.092283   0.308000     
## racePctWhite           -2.135769   3.531886   0.385240     
## racePctAsian            0.254106   0.844966   0.163850     
## racePctHisp             0.541173   1.551077   0.192650     
## agePct12t29             0.176217   1.083324   0.144440     
## agePct65up             -0.194398   1.228221   0.120090     
## numbUrban              -1.400553   1.989512   0.485690     
## pctUrban               -1.323449   1.859229   0.459960     
## medIncome               0.376474   2.008206   0.128390     
## pctWWage               -0.836679   2.331470   0.216670     
## pctWFarmSelf            0.008667   0.302906   0.093400     
## pctWInvInc              1.167247   2.260643   0.294420     
## pctWSocSec             -0.264674   1.461475   0.135510     
## pctWPubAsst             7.259389   2.470309   0.964970     
## pctWRetire              0.020054   0.387573   0.087040     
## medFamInc               0.485311   2.313313   0.147520     
## whitePerCap            -1.359176   2.564734   0.314340     
## blackPerCap            -0.055486   0.337129   0.106680     
## indianPerCap            0.024266   0.229567   0.078770     
## AsianPerCap            -0.201856   0.582698   0.171880     
## OtherPerCap             0.532231   0.886121   0.337600     
## HispPerCap              0.008384   0.329801   0.084070     
## NumUnderPov            -0.150960   2.120112   0.146180     
## PctPopUnderPov         -1.717400   2.847865   0.357040     
## PctLess9thGrade        -3.367505   2.775747   0.692710     
## PctBSorMore            -0.207695   0.993985   0.129900     
## PctUnemployed           0.185828   0.817010   0.114840     
## PctEmploy              -0.170923   0.865615   0.121190     
## PctEmplManu             1.013548   1.303923   0.456680     
## PctEmplProfServ        -0.007511   0.464698   0.095960     
## PctOccupMgmtProf       -0.308382   1.101401   0.155170     
## MalePctNevMarr          0.465209   1.278250   0.199760     
## TotalPctDiv             7.236784   1.969124   0.992030     
## PersPerFam             -0.172712   1.306106   0.110760     
## PctFam2Par             -0.523553   1.773577   0.160890     
## PctWorkMom             -0.122904   0.543521   0.127420     
## PctKidsBornNeverMar     0.293233   1.083908   0.135330     
## NumImmig                4.935297   3.984730   0.684630     
## PctImmigRecent         -0.032099   0.309089   0.084000     
## PctRecentImmig         -0.066448   0.880221   0.115770     
## PctSpeakEnglOnly        0.261269   1.716693   0.136920     
## PctNotSpeakEnglWell     0.443560   1.825018   0.163480     
## PctLargHouseFam         0.131478   0.812863   0.110410     
## PersPerOccupHous        0.409595   1.696769   0.158670     
## PersPerOwnOccHous       0.167416   0.931169   0.118440     
## PersPerRentOccHous      0.330763   1.032593   0.159930     
## PctPersOwnOccup        -0.074182   1.087310   0.104840     
## PctPersDenseHous        0.327026   1.279110   0.141530     
## PctHousLess3BR         -0.485907   1.343148   0.188420     
## MedNumBR               -0.362093   0.912037   0.206510     
## HousVacant              0.070922   0.412078   0.101800     
## PctHousOccup           -0.039648   0.345067   0.098730     
## PctHousOwnOcc           0.031382   0.944784   0.091080     
## PctVacantBoarded        9.038685   1.113651   0.999260     
## PctVacMore6Mos         -0.069940   0.409732   0.112260     
## MedYrHousBuilt         -0.010239   0.437252   0.108930     
## PctHousNoPhone         -0.680234   1.543345   0.229860     
## PctWOFullPlumb         -0.378604   0.842466   0.237070     
## OwnOccLowQuart          0.075807   1.828055   0.120300     
## OwnOccMedVal            1.213120   4.087233   0.204600     
## OwnOccHiQuart          -0.854063   3.116338   0.157850     
## RentLowQ                0.634005   1.666013   0.201740     
## RentMedian              0.052598   1.373276   0.102600     
## RentHighQ              -0.263229   1.492173   0.128260     
## MedRent                 0.148903   1.323720   0.114010     
## MedRentPctHousInc       1.151072   1.504447   0.460390     
## MedOwnCostPctInc       -0.130374   0.637545   0.133390     
## MedOwnCostPctIncNoMtg   0.134915   0.517961   0.134800     
## NumInShelters           3.840262   1.391839   0.957460     
## NumStreet               0.015178   0.342480   0.088550     
## PctForeignBorn         -2.966967   3.653157   0.501370     
## PctBornSameState       -0.785013   1.790411   0.247690     
## PctSameHouse85         -0.203785   0.821113   0.133750     
## PctSameCity85          -0.138763   0.662226   0.125790     
## PctSameState85          0.613753   1.513568   0.225480     
## LandArea                0.260845   0.816557   0.175020     
## PopDens                -0.144130   0.599277   0.129070     
## PctUsePubTrans         -0.121727   0.523761   0.131510     
## LemasPctOfficDrugUn    -0.007959   0.270418   0.085840     
## agePct22t29            -0.598228   1.327026   0.248520

10.4.1 individual plot

probne0 > 0.2

survivors = which(coef.gprior$probne0 > 0.2)
plot(coef.gprior, subset = survivors, ask = F)

10.4.2 coefficient plot

plot(confint(coef.gprior, parm = survivors))

## NULL

10.5 Prediction

muhat.bma <- fitted(fit.gprior, estimator = "BMA")
bma <- predict(fit.gprior, estimator = "BMA", newdata = data)

result_data = original_data %>%
  mutate(pred_y=bma$fit)
## Warning: Ignoring 91 observations